Question

1.设隐函数y=y(x)是由方程x=ln(x+y)所确定,试求dy/dx.

Answer 1

1.对x=ln(x+y）求微分,得

dx=(dx+dy)/(x+y),

∴dy=(x+y-1)dx,

∴dy/dx=x+y-1.

2.e^(xy)+y^3-5x=0,①

求微分得e^(xy)*(ydx+xdy)+3y^2*dy-5dx=0,

∴[xe^(xy)+3y^2]dy=[5-ye^(xy)]dx,

∴dy/dx=[5-ye^(xy)]/[xe^(xy)+3y^2].

由①,x=0时y=-1.

∴dy/dx|x=0

=6/3=2.