Question

How do you find f'(x) for `f(x) = (ln x)^8`?

Answer 1

This shall be accomplished by the chain rule.

Explanation:

Let, `y = f(x)` where `f(x) = (Ln x)^8` .

We have to evaluate `(dy)/dx`.
Now, let `t = Ln x implies y = t^8`

Now, let us differentiate `y` with respect to `x`,

`(dy)/dx = (dy)/dt*(dt)/dx`

`implies (dy)/dx = 8t^7*d/dx(Ln x)`

`implies (dy)/dx = 8(Ln x)^7/x`, which is the derivative we were looking for.