logarithmic differentiation
TRANSCRIPT
Left Hand Side (while finding )
Right Hand Side (while finding )
Therefore:
We first find y in terms of x.
This is not for the purpose of
Differentiation, but for a reason seen later.
This is an example of Implicit
Differentiation.
When differentiating a y value with respect to y, you
may differentiate each y term as if it were with
respect to x, however, you must then multiply the
derivative by .
This is an example of the Product Rule: You take a non-differentiable product, and split it up into two differentiable terms (in this case 3x and ln x). Equate one term to u, and another to v (or equivalent),
and then differentiate u and v, individually, which results in ,
respectively. , in this instance, is equal to: .
The result to this equation is as follows…
Putting the Left and Right hand sides back together
gives us the following: Multiply both sides by y to get a value of y on the right
hand side. You can then substitute the value of y in terms of x into
the equation. Thus, we now have the
derivative of y in terms of only x.