The derivative of 2/x is equal to -2/x^{2}. 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(x^{n}) = nx^{n-1}.

= -2 × x^{-2}

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

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

Have You Read These Derivatives?

Derivative of 1/x | Derivative of √x |

Derivative of 1/x^{2} | Derivative of 1/2x |

Derivative of 2^{x} | Derivative of 10^{x} |

## FAQs

### Q1: What is the derivative of 2/x?

Answer: The derivative of 2/x (2 divided by x) is equal to -2/x^{2}.

### Q2: If y=2/x, then find dy/dx.

Answer: If y=2/x then dy/dx= -2/x^{2}, that is, d/dx(2/x) = -2/x^{2}.