# Math Help - function question

1. ## function question

find f'''(x) if f(x)=xsinx

is it just simply f'''(x)=-xcosx

2. no you need to use the product rule...if f and g are functions, then the derivative of $f\cdot g=f'\cdot g+f\cdot g'$

Use that rule and try again

3. so f'(x)= sinx+xcosx
f''(x)=cosx+(cosx-xsinx)
f'''(x)=-sinx-sinx-cosx
i dont think i did that right. can anyone help me. calc is kicking me hard

4. $f(x)=x\sin x$

$f'(x)= (x)'\cdot \sin x+x\cdot (\sin x)'$

$=1\cdot \sin x+x\cdot \cos x$

$=\sin x+x\cos x$

$f''(x)=(\sin x)'+(x)'\cos x+x\cdot (\cos x)'$

$=\cos x+\cos x-x\sin x=2\cos x-x\sin x$

$f'''(x)=(2\cos x)'+(-x)'\sin x +(-x)(\sin x)'$

$=-2\sin x-\sin x-x\cos x=-3\sin x-x\cos x$

5. thank you very much.