If f(x)=sinx^2, find f'(x) and hence find integrate(xcosx^2)dx

okay i think i'm having a bit of problem with the front part.. is it the same as sin^2x??

Question

If f(x)=sinx^2, find f'(x) and hence find integrate(xcosx^2)dx

okay i think i'm having a bit of problem with the front part.. is it the same as sin^2x??

kainui · Answer

So is this your integral? $$\LARGE \int\limits x \cos (x^2)dx$$ I'm just making sure the squared part is there.

anonymous · Answer

wait dang the prime means to differentiate doesn't it?

anonymous · Answer

oh yes yup

anonymous · Answer

does that make f'(x)=cos2x?

kainui · Answer

Almost, do know what the chain rule is? Try to use the definition to get the right answer

anonymous · Answer

it isn't cos2x? D:

kainui · Answer

So for example if I have $$\LARGE f(x)=\sin(x^3)$$ then the derivative is $$\LARGE f'(x)=\cos(x^3)*3x^2$$ since I took the derivative of the outside and multiplied it by the derivative of the inside.

anonymous · Answer

2sincosx^2?