设y=cosx+xe^y,则x=0时,dy/dx=?

Question

设y=cosx+xe^y,则x=0时,dy/dx=?

Answer 1

x=0时,y=1
dy/dx=-sinx+e^y+(xe^y)dy/dx
所以dy/dx=(-sinx+e^y)/(1-xe^y)
把x=0,y=1代入上式,得dy/dx=e