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

1 Answer
Jul 29, 2015

Answer:

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.