Question

How do you differentiate `sin^2(x) * cos^2(x)`?

Answer 1

`(d y)/(d x)=2 sin x cos^3 x-2 cos x*sin^3 x`

Explanation:

`y=sin^2 x*cos^2 x`

`(d y)/(d x)=(sin^2 x)^'*cos^2 x+(cos^2 x)^'*sin^2 x`

`(sin^2 x)^'=2sin x cos x`

`(cos^2 x)^'=-2sin x cos x`

`(d y)/(d x)=2 sin x cos x* cos^2 x-2 sin x cos x*sin^2 x`

`(d y)/(d x)=2 sin x cos^3 x-2 cos x*sin^3 x`