[Solved] What is the Derivative of 4/x?

The derivative of 4/x is equal to -4/x². In this post, we will find the derivative of 4 divided by x by the power rule.

The derivative of 4/x is denoted by d/dx(4/x), and its formula is given by

$\dfrac{d}{dx}(\dfrac{4}{x})= – \dfrac{4}{x^2}$.

Derivative of 4/x

Question: Find the Derivative of 4/x.

Answer: We can express 4/x as 2x^-1 by the rule of indices. So the derivative of 4/x is -4/x² by the power rule of derivatives.

Explanation:

$\dfrac{d}{dx}(\dfrac{4}{x})$ = $4 \dfrac{d}{dx}(\dfrac{1}{x})$

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

= 4 × (-x^-1-1) by the power rule of derivatives d/dx(xⁿ) = nx^n-1.

= -4 x^-2

= $- \dfrac{4}{x^2}$.

Therefore, the derivative of 4/x is equal to -4/x², and this is obtained by the power rule of derivatives.

Have You Read These Derivatives?

Derivative of 1/x	Derivative of 2/x
Derivative of 3/x	Derivative of 1/2x
Derivative of 1/x2	Derivative of 2x

FAQs