Question

微积分微积分

可以只写一个告诉回答那个手写图片

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Answer 1

如下

Answer 2

z=(x^2+y^2). e^[-arctan(y/x) ]
lnz = ln(x^2+y^2) - arctan(y/x)
(1/z)∂z/∂y = 2y/(x^2+y^2) - [1/(1+(y/x)^2)] .(1/x)
= 2y/(x^2+y^2) - x/(x^2+y^2)
=(2y-x)/(x^2+y^2)
∂z/∂y = [(2y-x)/(x^2+y^2)] .(x^2+y^2). e^[-arctan(y/x) ]
= (2y-x). e^[-arctan(y/x) ]
∂^2z/∂x∂y
=∂/∂x (∂z/∂y)
= -e^[-arctan(y/x) ] +(2y-x). e^[-arctan(y/x) ] . [-1/(1 +(y/x)^2] . (-y/x^2)
=-e^[-arctan(y/x) ] +[y(2y-x)/(x^2+y^2)]. e^[-arctan(y/x) ]