求z=Intan(x/y)的偏导数的过程谁知道求?我有最终答案,最好把涉及的三角函数告诉我(2/y)csc(2x/y)和-(2x/(y^2))csc(2x/y)

Question

求z=Intan(x/y)的偏导数的过程
谁知道求?我有最终答案,最好把涉及的三角函数告诉我
(2/y)csc(2x/y) 和 -(2x/(y^2))csc(2x/y)

Answer 1

z=Intan(x/y)
∂z/∂x=[tan(x/y)]'/tan(x/y)= (1/y)[sec²(x/y)]/tan(x/y)
= (1/y)/[cos(x/y)sin(x/y)=(2/y)/sin(2x/y)=(2/y)csc(2x/y)
∂z/∂y=[tan(x/y)]'/tan(x/y)= (-x/y^2)[sec²(x/y)]/tan(x/y)
= (-x/y^2)/[cos(x/y)sin(x/y)=(-2x/y^2)/sin(2x/y)=(-2x/y^2)csc(2x/y)