Given the function f(x) = (x^2)sin(x), find f'(x).
The function f(x) is a product of 2 functions of x, so when we differentiate it, we need to use the product rule.
The product rule states that for a function f(x) = g(x)*h(x), f'(x) is given by g(x)*h'(x) + h(x)*g'(x).
If we break f(x) up into two parts and let g(x) = x2 and h(x) = sin(x) then we can find g'(x) and h'(x).
We find that g'(x) = 2x and h'(x) = cos(x). Substituting these values into the product rule, we get:
f'(x) = x2cos(x) + 2xsin(x).
