# Derivative of a Reciprocal

How to find the derivative of a reciprocal 1/g(x): formula (reciprocal rule), 1 example, and its solution.

## Formula

### Derivative of 1/g(x): Reciprocal Rule

The derivative of 1/g(x) is -g'(x)/[g(x)]^{2}.

## Example

### Example

### Solution

1/(x^{3} + 2x) is the reciprocal of (x^{3} + 2x).

So y' is equal to ...

Write - and the fraction bar.

Write, the derivative of (x^{3} + 2x), 3x^{2} + 2

in the numerator.

Derivative of a Polynomial

Write, the square of (x^{3} + 2x), (x^{3} + 2x)^{2}

in the denominator.

So y' = -(3x^{2} + 2)/(x^{3} + 2x)^{2} is the derivative of the function.