设z=xF(xy^2,e^（x的平方）再乘y),F有连续偏导数,求Zx,Zy

题目

设z=xF(xy^2,e^（x的平方）再乘y),F有连续偏导数,求Zx,Zy

答案

是这个意思吗：z=xF(xy²,(e^x²)y),那么记F=F(xy²,(e^x²)y),F1=dF/d(xy²),F2=dF/d[(e^x²)y],Fx=F1*d(xy²)/dx+F2*d[(e^x²)y]/dx=y²F1+2xy(e^x²)F2Fy=F1*d(xy²...