若z(x,y)=f(x^2+y^2,x-y),其中f具有连续偏导数,求Ȣz⼀Ȣx,Ȣz⼀Ȣy.

求大神帮忙解答这个难题,衷心感谢!!
2025-01-20 04:38:21
推荐回答(1个)
回答1:

z=f(x^2,g(y/x))
az/ax=f`1(2x)+f`2g`(y/x)(-y/x²)
=2xf`1-y/x²f`2 g`(y/x)
a^2z/axay
=2x[f``11*0+f``12g`(y/x)(1/x)]-{1/x²f`2g`(y/x)+y/x²g`(y/x)[f``12*0+f``22g`(y/x)/x]+y/x²f`2g``(y/x)/x}
=2x[f``12g`(y/x)(1/x)]-{1/x²f`2g`(y/x)+y/x²g`(y/x)[f``22g`(y/x)/x]+y/x²f`2g``(y/x)/x}