Question

What is the derivative of `tan^2(3x)`?

Answer 1

`d/dx tan^2(3x) = 6sec^2(3x)tan(3x)`

Explanation:

In order to differentiate this function, we have to apply the chain rule twice:

`d/dx tan(f(x))= sec^2(f(x)) f'(x)`

`d/dx [tan(x)]^n = n[tan(x)]^(n-1)sec^2x`

So, applying these two rules, we get:

`d/dx tan^2(3x) = 2tan(3x)sec^2(3x)(3)=6sec^2(3x)tan(3x)`