# Differentiate the function f (x) = ln x^{1 / 5}.

## Question:

Differentiate the function {eq}\displaystyle f (x) = \ln x^{\dfrac 1 5} {/eq}.

## Differentiation

This question is from the differentiation and we have to differentiate it. We will use the chain rule to solve it.

{eq}\Rightarrow \ f(x)=\ln(x)^{\frac{1}{5}}\\ \text{differentiate with respect to x}\\ \Rightarrow \ f'(x)=\frac{1}{5\ln^{\frac{4}{5}}(x)}\frac{d}{dx}\ln(x)\\ \Rightarrow \ f'(x)=\frac{1}{5x\ln^{\frac{4}{5}}(x)} {/eq}