Question

What is the derivative of `sin^2(x)cos^2(x)`?

Answer 1

`=2sinxcosxcos2x`

Explanation:

Using the product rule, together with the power rule, we obtain :

`d/dx [sin^2x*cos^2x]=sin^2x*2cosx*(-sinx) +cos^2x*2sinx*cosx`

`=2sinxcosx(cos^2x-sin^2x)` . (Took out common factor)

`=2sinxcosxcos2x` . (Used half angle identity)