The derivative of 3/x is equal to -3/x^{2}. The derivative formula of 3/x (3 divided by x) is given by as follows:

$\dfrac{d}{dx}(\dfrac{3}{x})= – \dfrac{3}{x^2}$.

## Derivative of 3/x

**Question:** What is the Derivative of 3/x?

*Answer:* As 3/x can be expressed as 3x^{-1}, applying the power rule, the derivative of 3/x is equal to -3/x².

**Explanation:**

$\dfrac{d}{dx}(\dfrac{3}{x})$ = $\dfrac{d}{dx}(3x^{-1})$

= $3 \dfrac{d}{dx}(x^{-1})$

= 3 × -x^{-1-1} by the power rule of derivatives

= -3x^{-2}

= $-\dfrac{3}{x^2}$.

So the derivative of 3/x is equal to -3/x^{2}, and this is proved by the power rule of derivatives.

Related Derivatives:

Derivative of 1/x | Derivative of 2/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 3/x?

Answer: The derivative of 3/x is equal to -3/x^{2}.

### Q2: If y=3/x, then find dy/dx.

Answer: If y=3/x then dy/dx= -3/x^{2}, that is, d/dx(3/x) = -3/x^{2}.