Question

高数：y=f(e^x)e^f(x),其中f可微,则dy=____d(e^x)

Answer 1

t=e^x x=lnt

y=f(t)e^f(lnt)

dy/dt=f'(t)e^f(lnt)+f(t)e^f(lnt)f'(lnt)/t

dy/d(e^x)=f'(e^x)e^f(x)+f(e^x)e^f(x)f'(x)/e^x

dy=f'(e^x)e^f(x)+f(e^x)e^f(x)f'(x)/e^x d(e^x)