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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.

Answer and Explanation:

{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}


Learn more about this topic:

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Solving Partial Derivative Equations

from GRE Math: Study Guide & Test Prep

Chapter 14 / Lesson 1
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