Question

How do you differentiate `sin^3 4x`?

Answer 1

`d/dx sin^3(4x)=12sin^2(4x)cos(4x)`

Explanation:

Using the chain rule:

`d/dx sin^3(4x) = d/dx(sin(4x))^3`

`=3(sin(4x))^2(d/dxsin(4x))`

`=3sin^2(4x)(cos(4x)(d/dx4x))`

`=3sin^2(4x)cos(4x)(4)`

`=12sin^2(4x)cos(4x)`