Question

How do you find the derivative of `sin(x^2)cos(x^2)`?

Answer 1

`y'= -2xsin^2(x^2)+2xcos^2(x^2)`

Explanation:

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

Use product rule and chain rule

`f=sin(x^2), g=cos(x^2)`

`f'=cos(x^2)(2x), g'=-sin(x^2)(2x)`

`y'=fg'+gf'`

`y'= -2xsin^2(x^2)+2xcos^2(x^2)`