1、已知f(x) =xsinx+x²cosx，求fˊ(x). 2、已知f(x) =xlnx+sinx/x，求fˊ(x).

Question

写一下过程

Answer 1

(1) f'(x)=(x)'sinx+x(sinx)'+(x2)‘cosx+x2(cosx)'
=sinx+xcosx+2xcosx-x2sinx
=3xcosx+(1-x2)sinx
(2) f'(x)=(x)'lnx+x(lnx)'+[(sinx)'x-sinx(x)']/(x2)
=lnx+1+(xcosx-sinx)/x2

Answer 2

1、f'(x)=（1-x^2)sinx+3xcosx
2、f'(x)=Inx+1+（cosx*x-sinx）/x^2

Answer 3

1、f'(x)=sinx+xcosx+2xcosx-x^2sinx
2、f'(x)=Inx+1+cosx/x-sinx/x^2