Question

If `y = cosx^3sin^2(x^5)`, what is `dy/dx`?

Answer 1

See explanation

Explanation:

According to the product rule,
`d/dx[f(x)*g(x)]=f(x)*g'(x)+g(x)*f'(x)`, where `f(x) = cos(x^3)` and `g(x) = sin^2 (x^5)`

Therefore (be careful with the chain rule),
#d/dx [cosx^3 *sin^2 (x^5)] = cosx^3 * 2sin(x^5) * cos(x^5) * 5x^4 +sin^2(x^5) * -sin(x^3)*3x^2#

That can be re-written or simplified as:
`x^2sin(x^5)(10x^2cos(x^3)cos(x^5)-3sin(x^3)sin(x^5))`