Question

设sinxy+e^xy=ax,求dy/dx

Answer 1

sinxy+e^xy=ax两遍对x求导,得

(y+xdy/dx)cosxy+(y+xdy/dx)e^xy=a

(y+xdy/dx)(cosxy+e^xy)=a

由此得到

dy/dx=a/[(cosxy+e^xy)x]-y/x