logarithmic differentiation

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.