What is the Derivative of 2/x?

The derivative of 2/x is equal to -2/x². Here, we will learn how to find the derivative of 2 divided by x. The derivative formula of 2/x is given by

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

Derivative of 2/x

Question: Find the Derivative of 2/x.

Answer: We can express 2/x as 2x^-1. So by the power rule, the derivative of 2/x is equal to -2/x².

Explanation:

$\dfrac{d}{dx}(\dfrac{2}{x})$

= $2 \dfrac{d}{dx}(\dfrac{1}{x})$

= $2 \dfrac{d}{dx}(x^{-1})$

= 2 × (-1 ⋅ x^-1-1) by the power rule of derivatives d/dx(xⁿ) = nx^n-1.

= -2 × x^-2

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

Hence, the derivative of 2/x is -2/x², and this is obtained by the power rule of derivatives.

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