Step 1
We are ed to differentiate the given function; to do this we have to use the power rule and remember our trid identities when it comes to taking the derivative.
f(x)=x^(2)*sin(x)
Step 2
We will have to remember that the derivative of sin(x) is cos(x)
f'(x)=x^(2)*sin(x)
=x^(2)*(d)/(dx)(sin(x))+(d)/(dx)(x^(2))*sin(x)
=x^(2)*cos(x)+2* x*sin(x)

Step 1 Let f(x)=(x^(2))(sin x) then f(x)=g(x)* h(x) The derivative of this function is given by f'(x)=(g'(x)* h(x))+(h'(x)* g(x)) The derivative of g(x) or x^(2) is g'(x)=2* x^(2-1)=2x The derivative of h(x) or sin x is h'(x)=cos x Applying the product rule: f'(x)=(g'(x)* h(x))+(h'(x)* g(x)) f'(x)=(2x(sin x))+(x^(2)(cos x)) f'(x)=2xsin x+x^(2)cos x Hence, the derivative of y=(x^(2))(sin x) is y'=2xsin x+x^(2)cos x