Question

What is the derivative of `tan^4 (x)`?

Answer 1

`d/dx[tan^4(x)]=4tan^3(x)sec^2(x)`

Explanation:

The overriding issue is the fourth power. You can deal with it through the chain rule:

`d/dx[u^4]=4u^3*u'`

Here, we have `u=tan(x)`, so

`d/dx[tan^4(x)]=4tan^3(x)*d/dx[tan(x)]`

Know that `d/dx[tan(x)]=sec^2(x)`, hence

`d/dx[tan^4(x)]=4tan^3(x)sec^2(x)`