设Z=f(x^2-y^2,e^xy),且f具有一阶连续偏导数,求z的一阶偏导数.

问题描述:

设Z=f(x^2-y^2,e^xy),且f具有一阶连续偏导数,求z的一阶偏导数.

令x^2-y^2=u,e^xy=vdZ=df/du(2xdx-2ydy)+df/dv(ye^xydx+xe^xydy)=(2xdf/du+ye^xydf/dv)dx+(xe^xydf/dv-2ydf/du)dy所以dZ/dx=2xdf/du+ye^xydf/dv,dZ/dy=xe^xydf/dv-2ydf/du