Question

How do you differentiate `f(x)=(1-x)tan^2(2x)` using the product rule?

Answer 1

Step by step working shown below.

Explanation:

`f(x)=(1-x)tan^2(2x)`

This problem would require product rule and chain rule.

The product rule.

`(uv)'=uv'+vu'`

`f'(x) = (1-x)d/dx(tan^2(2x))+tan^2(2x)d/dx(1-x)`

For derivating `tan^2(2x)` we need to use the chain rule.

`f'(x) = (1-x){2tan(2x)d/dx(tan(2x))} + tan^2(2x)(-1)`

`f'(x)=(1-x){2tan(2x)sec^2(2x)d/dx(2x)} - tan^2(2x)`

`f'(x) = (1-x){2tan(2x)sec^2(2x)(2)}-tan^2(2x)`

`f'(x)=4(1-x)tan(2x)sec^2(2x)-tan^2(2x)`