Question

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

Answer 1

`(sin 4x)/2`

Explanation:

`sin(x)cos(x) = (sin 2x)/2`
`\implies sin^2(x)cos^2(x) = (sin^2 2x)/4`

`((sin^2 2x)/4)' = 1/4 (2 sin 2x cos 2x (2) ) = sin 2x cos 2x = (sin 4x)/2`