设z=yarctany/x,求z/x,z/y

Question

如题所述

Answer 1

∂z/∂x
=y*∂(arctany/x) /∂x
=y* 1/(1+y²/x²) *∂(y/x) /∂x
=y* 1/(1+y²/x²) *(-y/x²)
= -y²/(x²+y²)
∂z/∂y
=arctan(y/x) +y*∂(arctany/x) /∂y
=arctan(y/x) +y* 1/(1+y²/x²) *∂(y/x) /∂y
=arctan(y/x) +y* 1/(1+y²/x²) *1/x
=arctan(y/x) + xy /(x²+y²)