Question

设u=sin(x+y),其中y=y(x)由方程ex+y=x=sinx确定,求du/dx.ex是e的x次

Answer 1

(e^x)+y=x+sinx

=> y=x+sinx-e^x

=> dy/dx=1+cosx-e^x

u=sin(x+y),

du/dx=cos(x+y)*(1+dy/dx)

=cos(x+y)*(1+1+cosx-e^x)

=cos(x+y)*(2+cosx-e^x)