Question

Derivative of (log x)^4 is

Answer 1

$\dfrac{d}{dx}\{(logx)^{4}\}=\dfrac{4}{x}(logx)^{3}$

Given data:

The function $y=(logx)^{4}$

To find:

$\dfrac{dy}{dx}$

Concept:

Before we solve this problem, we must know that,

• $\dfrac{d}{dx}(x^{n})=n\:x^{n-1}$ where n is a rational number.

• $\dfrac{d}{dx}(logx)=\dfrac{1}{x}$

• $\dfrac{d}{dx}(f(g(x)))=f'(g(x))\times g'(x)$

Step-by-step explanation:

Here, $y=(logx)^{4}$

Differentiating both sides with respect to x, we get

$\dfrac{dy}{dx}=\dfrac{d}{dx}(logx)^{4}$

$=4\:(logx)^{4-1}\:\dfrac{d}{dx}(logx)$

$=4\:(logx)^{3}\:\dfrac{1}{x}$

$=\dfrac{4}{x}(logx)^{3}$

This is the required derivative.

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