设z=f(xy,x^2+y^2),其中f具有连续的二阶偏导数,求α^2z/αxαy.
问题描述:
设z=f(xy,x^2+y^2),其中f具有连续的二阶偏导数,求α^2z/αxαy.
答
d²z/dxdy = d(df/dx)/dy = d(yf1+2xf2)/dy = f1+y(xf11+2yf12) + 2x(f21x+2yf22)
=f1+(2x²+xy)f12+4xyf22