Question

设函数u=f(xy,x/y),求:偏u/偏x,偏u/偏y?

Answer 1

∂u/∂x=[∂u/∂(xy)][d(xy)/dx]+[∂u/∂(x/y)][d(x/y)/dx]=yf₁'+(1/y)f₂'

∂u/∂y=[∂u/∂(xy)][d(xy)/dy]+[∂u/∂(x/y)][d(x/y)/dy]=xf₁'+(-x/y^2)f₂'