Question

How do you differentiate `f(x)=3(tan4x)^(1/2)` using the chain rule?

Answer 1

`6*(sec^2(4x))/(tan^(1/2)(4x))`

Explanation:

`tan(4x)=t`
`d/dt(3(t^(1/2)))=(3/2)*(t^(-1/2))`
`d/dx(t) = 4*sec^2(4x)`
combining them and converting t back we get
`6*(sec^2(4x))/(tan^(1/2)(4x))`