The derivative of 4/x is equal to -4/x^{2}. 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(x^{n}) = nx^{n-1}.

= -4 x^{-2}

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

Therefore, the derivative of 4/x is equal to -4/x^{2}, 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/x^{2} | Derivative of 2^{x} |

## FAQs

### Q1: What is the derivative of 4/x?

Answer: The derivative of 4/x (4 divided by x) is equal to -4/x^{2}.

### Q2: If y=4/x, then find dy/dx.

Answer: If y=4/x then dy/dx= -4/x^{2}.