设z=x^2y-xy^2,x=ucosv,y=usinv,求δz/δv ,δz/δu._数学解答

设z=x^2y-xy^2,x=ucosv,y=usinv,求δz/δv ,δz/δu.

人气：448 ℃　时间：2020-10-02 04:28:36

解答

δz/δv =δz/δx *δx/δv +δz/δy *δy/δv=(2xy-y^2)(-usinv)+(x^2-2xy)ucosv
δz/δu =δz/δx *δx/δu +δz/δy *δy/δu=(2xy-y^2)cosv+(x^2-2xy)sinv