Question

求函数z=(x+y)sin(x-y)的偏导数∂z/∂x,∂z/∂y

Answer 1

∂z/∂x只对x求导数,而把y看作一个常数,∂z/∂x=(x+y)'sin(x-y)+(x+y)sin(x-y)'=

sin(x-y)+(x+y)cos(x-y)

∂z/∂y只对y求导数,而把x看作一个常数,∂z/∂y=(x+y)'sin(x-y)+(x+y)sin(x-y)'

=sin(x-y)+(x+y)[-cos(x-y)]

=sin(x-y)-(x+y)cos(x-y)