设z=u^2v^2,而u=x-y,v=x+y,求dz/dx,dz/dy

问题描述:

设z=u^2v^2,而u=x-y,v=x+y,求dz/dx,dz/dy

由z=u²v²,其中u=x-y,v=x+y,
题型:求复合函数的偏导数:
z=(x-y)²(x+y)²,
dz/dx=(x-y)²×2(x+y)+2(x-y)(x+y)²
=2(x+y)(x-y)(x-y+x+y)
=4x(x+y)(x-y)
dz/dy=(x-y)²×2(x+y)+(x+y)²×[-2(x-y)]
=2(x+y)(x-y)(x-y-x-y)
=-4y(x+y)(x-y).