Question

What is the derivative of `f(x) = xcos(x^2)+x^2sin(x)`?

Answer 1

It is given that, `f(x)=xcos(x^2)+x^2sin(x)`

Applying product rule to each term,

`f'(x)=[x'*cos(x^2) + x*cos(x^2)']+[x^2'*sin(x)+x^2*sin(x)']`

`=>[cos(x^2) + x*-sin(x^2)*2x]+[2x*sin(x)+x^2*cos(x)]`

`=>cos(x^2) -2x^2sin(x^2)+2xsin(x)+x^2cos(x)`