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/(x3 + 2x) is the reciprocal of (x3 + 2x).

So y' is equal to ...
Write - and the fraction bar.

Write, the derivative of (x3 + 2x), 3x2 + 2
in the numerator.

Derivative of a Polynomial

Write, the square of (x3 + 2x), (x3 + 2x)2
in the denominator.

So y' = -(3x2 + 2)/(x3 + 2x)2 is the derivative of the function.