z=x*arctan(xy),求(dz/dx)|(1,1),(dz/dy)|(1,1)

题目

z=x*arctan(xy),求(dz/dx)|(1,1),(dz/dy)|(1,1)

答案

dz/dx=arctan(xy)+xy/[1+(xy)^2]
(dz/dx)|(1,1)=π/4+1/2
(dz/dy)|(1,1)=x^2/[1+(xy)^2]=1/2