Question: If z = f (u, v), where u = xy, v = y/x, and f has continuous second partial derivatives, show that ?2 - y.

If z = f (u, v), where u = xy, v = y/x, and f has continuous second partial derivatives, show that

д?2 - y². ду? д?z a²z -4uv дz + 2v до дх? ди ду

?2 - y. ? ?z az -4uv z + 2v ?

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Az z 0 Ju 22 z x2 J2 z 2 Thus y z Also x Az x Ju 2 z z v x2 x2 z Az u a2 z 2 since y xv y2 ... View full answer

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