Question

How do you differentiate `f(x)=3sqrt(tan4x^2)` using the chain rule?

Answer 1

`f'(x)=(12x)/(cos^2 4x^2 sqrt(tan4x^2))`

Explanation:

`f'(x)=3/(2sqrt(tan4x^2))*(tan4x^2)'=`

`3/(2sqrt(tan4x^2))*1/(cos^2 4x^2)(4x^2)'=`

`3/(2sqrt(tan4x^2))*1/(cos^2 4x^2)*8x=`

`(12x)/(cos^2 4x^2 sqrt(tan4x^2))`