The derivative of 1/x^{n} (1 by x power n) is equal to -n/x^{n+1}. Here we learn how to find the derivative of 1 divided by x to the n.

The derivative formula of 1/x^n is given by

$\dfrac{d}{dx} \big( \dfrac{1}{x^n}\big) = -\dfrac{n}{x^{n+1}}$.

## Derivative of 1/x^{n}

**Answer:** The derivative of 1/x^{n} is equal to -n/x^{n+1}.

**Explanation:**

By the rule of indices, we have that

1/x^{n} = x^{-n}

Differentiating both sides, we get that

$\dfrac{d}{dx} \big( \dfrac{1}{x^n}\big)$

= $\dfrac{d}{dx} \big( x^{-n} \big)$

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

= $-\dfrac{n}{x^{n+1}}$.

So the derivative of 1 by x to the power n is equal to -n/x^{n+1}, and this is obtained by the power rule of derivatives.

More Derivatives:

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

Derivative of 1/x^{2} | Derivative of ln(ln x)

## FAQs

### Q1: What is the derivative of 1 by x power n?

Answer: The derivative of 1 by x power n is equal to -n/x^{n+1}.