Question

How do you take the derivative of `tan^2(5x)`?

Answer 1

`= 10tan 5x sec^2 5x`

Explanation:

Let `t = 5x`.

`frac{d}{dx}tan^2 5x = frac{dt}{dx}frac{d}{dt}tan^2 t`.

Product rule: `frac{d}{dt}tan^2 t = 2tan t\frac{d}{dt}tan t`.
Now `\frac{d}{dt} tan t = sec^2 t`.

Hence `frac{d}{dx}tan^2 5x = 10tan 5x sec^2 5x`