求z=x•y•根号下(r^2-x^2-y^2)的偏导数

Question

求z=x•y•根号下(r^2-x^2-y^2)的偏导数

Answer 1

z=x•y•√(r^2-x^2-y^2)
求z对x的偏导数时,只把x看作自变量,
∴z'(x)=y√(r^2-x^2-y^2)+xy•1/√(r^2-x^2-y^2)•(-x)
=y√(r^2-x^2-y^2)-(x^2)y/√(r^2-x^2-y^2)
同理
z'(y)=x√(r^2-x^2-y^2)-x(y^2)/√(r^2-x^2-y^2)