Question

How do you differentiate `g(x) = sqrt(x^2-x)sin^2x` using the product rule?

Answer 1

`(sin(x)(4(x-1)xcos(x)+(2x-1)sin(x)))/(2sqrt(x(x-1))`

Explanation:

We get by the product and the chain rule

`1/2(x^2-x)^(-1/2)*(2x-1)sin^2(x)+sqrt(x^2-x)*2sin(x)cos(x)`

`(sin(x)(4(x-1)x*cos(x)+(2x-1)*sin(x)))/(2sqrt(x(x-1))`