Question

How do you use the product rule to find the derivative of y=x2⋅sin(x)y=x^2*sin(x) ?

Answer 1

$(f(x)\cdot g(x))'=f'(x)\cdot g(x)+f(x)\cdot g'(x)\\\\ y=x^2\sin x\\ y'=2x\cdot \sin x+x^2\cdot \cos x\\ y'=x(2 \sin x+x\cos x)$