设z=aretan(y/x),则=∂2z/∂x∂y____.
(y2-x2)/(x2+y2)2。 解析:∂z/∂x=(arctan(y/x))x′=1/[1+(y/x)2]•(y/x)x′ =x2/(x2+y2)[-(y/x2))=-[y/(x2+y2)] ∂ 2z/∂x∂y=[-(y/(x2+y2))]y′=- [(x2+y2-2y2)/(x2+y2)2=(y2-x2)/(x2+y2)2
设z=aretan(y/x),则=∂2z/∂x∂y____.
(y2-x2)/(x2+y2)2。 解析:∂z/∂x=(arctan(y/x))x′=1/[1+(y/x)2]•(y/x)x′ =x2/(x2+y2)[-(y/x2))=-[y/(x2+y2)] ∂ 2z/∂x∂y=[-(y/(x2+y2))]y′=- [(x2+y2-2y2)/(x2+y2)2=(y2-x2)/(x2+y2)2