Question

`{x}^(2){sin x}^(2)`
find its derivative​

Answer 1

2x(sinx^2 + x^2cosx^2).

Explanation:

We use the product rule:

If u and v are functions of x then:-

d(uv)/dx = u dv/dx + v du/dx

So:

d(x^2 sinx^2)dx

= x^2 * d(sinx^2)/dx + sinx^2 * d(x^2)/dx

= x^2 * 2xcosx^2 + sinx^2 * 2x

= 2x^3cosx^2 + 2xsinx^2

= 2x(sinx^2 + x^2cosx^2).