Question

z=e^sin(xy)一阶偏导数

求详细过程，本人新手不会解

Answer 1

对x的偏导数其实就将y看成是常数，当成一阶导数来求就可以了：
∂z/∂x=e^sin(xy)*cos(xy)*y
对y的偏导数同理：
∂z/∂y=e^sin(xy)*cos(xy)*x

Answer 2

∂Z/∂x= y*cos(xy) -2cos(xy)*sin(xy)*y
= y*cos(xy) - y*sin(2xy)
∂Z/∂y= x*cos(xy) -2cos(xy)*sin(xy)*x
= x*cos(xy) - x*sin(2xy)

Answer 3

引用Along菲子的回答：
∂Z/∂x= y*cos(xy) -2cos(xy)*sin(xy)*y
= y*cos(xy) - y*sin(2xy)
∂Z/∂y= x*cos(xy) -2cos(xy)*sin(xy)*x
= x*cos(xy) - x*sin(2xy)

看下面，别被这个答案搞昏