设z=arctan(uv),而u=x-2y,v=y+2x,求z对x的偏倒,z对y的偏倒亲爱的

Question

设z=arctan(uv),而u=x-2y,v=y+2x,求z对x的偏倒,z对y的偏倒
亲爱的

Answer 1

az/ax= 1/(1+u²v²) ·v·1+1/(1+u²v²) ·u·2
=(y+2x)/[1+(x-2y)²(y+2x)²] +2(x-2y)/[1+(x-2y)²(y+2x)²]
=(4x-3y)/[1+(x-2y)²(y+2x)²]
az/ay= 1/(1+u²v²) ·v·(-2)+1/(1+u²v²) ·u·1
=-2(y+2x)/[1+(x-2y)²(y+2x)²] +(x-2y)/[1+(x-2y)²(y+2x)²]
=(-3x-4y)/[1+(x-2y)²(y+2x)²]