F(x,y,z)=(x/y)^1/z,df(1,1,1)=

Question

F(x,y,z)=(x/y)^1/z,df(1,1,1)=

Answer 1

∂f/∂x=1/z*1/y*(x/y)^1/z∂f/∂y=-1/z*x/y^2*(x/y)^1/z∂f/∂z=ln(x/y)*(x/y)^1/zdf=∂f/∂x*dx+∂f/∂y*dy+∂f/∂z*dz=dx+dy