已知f'(x)=Inx,求[f(sinx)]'

已知f'(x)=Inx,求[f(sinx)]'
已知f'(x)=Inx,求[f(sinx)]'

已知f'(x)=Inx,求[f(sinx)]'
令t=lnx,则x=e^t,dx=e^tdt
∫lnxdx
=∫t*e^tdt
=∫td(e^t)
=t*e^t-∫e^tdt
=t*e^t-e^t+C
=(t-1)e^t+C
=(lnx-1)x+C
C为任意常数
[f(sinx)]'=1/x*x+lnx*1=lnx+1