11X1 T09 06 quotient & reciprocal rules (2011)

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  • Calculus Rules

  • Calculus Rules3. Quotient Rule

    2 d u vu uvdx v v

  • Calculus Rules3. Quotient Rule

    SQUARE the BOTTOM, write down the BOTTOM and DIFF the TOP, MINUS write down the TOP and DIFF the BOTTOM

    2 d u vu uvdx v v

  • Calculus Rules3. Quotient Rule

    SQUARE the BOTTOM, write down the BOTTOM and DIFF the TOP, MINUS write down the TOP and DIFF the BOTTOM e.g.

    1 2xi yx

    2 d u vu uvdx v v

  • Calculus Rules3. Quotient Rule

    SQUARE the BOTTOM, write down the BOTTOM and DIFF the TOP, MINUS write down the TOP and DIFF the BOTTOM e.g.

    1 2xi yx

    21 2 1 2

    1 2x xdy

    dx x

    2 d u vu uvdx v v

  • Calculus Rules3. Quotient Rule

    SQUARE the BOTTOM, write down the BOTTOM and DIFF the TOP, MINUS write down the TOP and DIFF the BOTTOM e.g.

    1 2xi yx

    21 2 1 2

    1 2x xdy

    dx x

    21 2 2

    1 2x xx

    2 d u vu uvdx v v

  • Calculus Rules3. Quotient Rule

    SQUARE the BOTTOM, write down the BOTTOM and DIFF the TOP, MINUS write down the TOP and DIFF the BOTTOM e.g.

    1 2xi yx

    21 2 1 2

    1 2x xdy

    dx x

    21 2 2

    1 2x xx

    2 d u vu uvdx v v

    21

    1 2x

  • Calculus Rules3. Quotient Rule

    SQUARE the BOTTOM, write down the BOTTOM and DIFF the TOP, MINUS write down the TOP and DIFF the BOTTOM e.g.

    1 2xi yx

    21 2 1 2

    1 2x xdy

    dx x

    21 2 2

    1 2x xx

    2

    2 4

    xii yx

    2 d u vu uvdx v v

    21

    1 2x

  • Calculus Rules3. Quotient Rule

    SQUARE the BOTTOM, write down the BOTTOM and DIFF the TOP, MINUS write down the TOP and DIFF the BOTTOM e.g.

    1 2xi yx

    21 2 1 2

    1 2x xdy

    dx x

    21 2 2

    1 2x xx

    2

    2 4

    xii yx

    1 1

    2 22 2

    2

    14 2 2 4 224

    x x x xdydx x

    2 d u vu uvdx v v

    21

    1 2x

  • Calculus Rules3. Quotient Rule

    SQUARE the BOTTOM, write down the BOTTOM and DIFF the TOP, MINUS write down the TOP and DIFF the BOTTOM e.g.

    1 2xi yx

    21 2 1 2

    1 2x xdy

    dx x

    21 2 2

    1 2x xx

    2

    2 4

    xii yx

    1 1

    2 22 2

    2

    14 2 2 4 224

    x x x xdydx x

    2 d u vu uvdx v v

    21

    1 2x

    1 1

    2 2 22 2

    2

    2 4 2 44

    x x xx

  • Calculus Rules3. Quotient Rule

    SQUARE the BOTTOM, write down the BOTTOM and DIFF the TOP, MINUS write down the TOP and DIFF the BOTTOM e.g.

    1 2xi yx

    21 2 1 2

    1 2x xdy

    dx x

    21 2 2

    1 2x xx

    2

    2 4

    xii yx

    1 1

    2 22 2

    2

    14 2 2 4 224

    x x x xdydx x

    2 d u vu uvdx v v

    21

    1 2x

    1 1

    2 2 22 2

    2

    2 4 2 44

    x x xx

    1

    2 2 22

    2

    2 4 44

    x x xx

  • Calculus Rules3. Quotient Rule

    SQUARE the BOTTOM, write down the BOTTOM and DIFF the TOP, MINUS write down the TOP and DIFF the BOTTOM e.g.

    1 2xi yx

    21 2 1 2

    1 2x xdy

    dx x

    21 2 2

    1 2x xx

    2

    2 4

    xii yx

    1 1

    2 22 2

    2

    14 2 2 4 224

    x x x xdydx x

    2 d u vu uvdx v v

    21

    1 2x

    1 1

    2 2 22 2

    2

    2 4 2 44

    x x xx

    1

    2 2 22

    2

    2 4 44

    x x xx

    2 2

    84 4x x

  • 4. Reciprocal Rule 2 d k kvdx v v

  • 4. Reciprocal Rule 2 d k kvdx v v

    MINUS the DERIVATIVE on the FUNCTION SQUARED

  • 4. Reciprocal Rule 2 d k kvdx v v

    MINUS the DERIVATIVE on the FUNCTION SQUARED

    21e.g. i y x

  • 4. Reciprocal Rule 2 d k kvdx v v

    MINUS the DERIVATIVE on the FUNCTION SQUARED

    21e.g. i y x4

    2dy xdx x

  • 4. Reciprocal Rule 2 d k kvdx v v

    MINUS the DERIVATIVE on the FUNCTION SQUARED

    21e.g. i y x4

    2dy xdx x

    32x

  • 4. Reciprocal Rule 2 d k kvdx v v

    MINUS the DERIVATIVE on the FUNCTION SQUARED

    21e.g. i y x4

    2dy xdx x

    32x

    26 4 3ii y x

  • 4. Reciprocal Rule 2 d k kvdx v v

    MINUS the DERIVATIVE on the FUNCTION SQUARED

    21e.g. i y x4

    2dy xdx x

    32x

    26 4 3ii y x

    226 8

    4 3

    xdydx x

  • 4. Reciprocal Rule 2 d k kvdx v v

    MINUS the DERIVATIVE on the FUNCTION SQUARED

    21e.g. i y x4

    2dy xdx x

    32x

    26 4 3ii y x

    226 8

    4 3

    xdydx x

    2248

    4 3x

    x

  • 4. Reciprocal Rule 2 d k kvdx v v

    MINUS the DERIVATIVE on the FUNCTION SQUARED

    21e.g. i y x4

    2dy xdx x

    32x

    26 4 3ii y x

    226 8

    4 3

    xdydx x

    2248

    4 3x

    x

    Exercise 7G; 1aceg, 2, 4a, 6a, 8a

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