calculus one – implicit differentiation – section 2 · calculus one – implicit...
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Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25
Calculus One – Implicit Differentiation – Section 2.5
To determine derivatives implicitly, differentiate term by term, using y′ (similar to u′ in the
chain rule) for any term containing a y-variable. Then solve for y′ .
Together from power-point You try.
1. 3y2
+ 2x3 – 14 = 0 2. y
3 + y
2 – 5y – x
2 = -4
3. 2y3 + y
2 – x = 0 4. 3x
2 + y -2 = 0
5. 3x4 + y – 2 = 0 6. x
2 + y
2 = 4
7. 2x3y – x
3 + 5 = 0 8. 3xy
2 – 8.23 = 0
Find the slope of the tangent line (AKA evaluate the derivative) at the indicated point. (2,1)
9. 3xy – 2x – 2 = 0 10. 2y + xy – 10 = 0
At (2,1) At (3,2)
Use implicit differentiation with trig functions.
11. tan x = y – x 12. cox x + y = sin y
13. x = cos (xy) 14. sin (xy) + 2cos3x = 12
Homework: Page 146, problems 1-11 odd, 15, 21, 25