设z=arctan(x/y) x=u+v y=u-v 验证δz/δu+δz/δv=(u-v)/(u^2+v^2)

题目

设z=arctan(x/y) x=u+v y=u-v 验证δz/δu+δz/δv=(u-v)/(u^2+v^2)

答案

δz/δu =δz/δx*δx/δu+δz/δy*δyδu=(y-x)/(y^2+x^2)
δz/δv=δz/δx*δx/δv+δz/δy*δyδv=(y+x)/(y^2+x^2)
左=2y/(x^2+y^2)=2(u-v)/2(u^2+v^2)=右
PS:上课能好好听么亲