设z=u^2cosv^2,u=x+y,v=xy,求dz/dx,dz/dy.高数题

问题描述:

设z=u^2cosv^2,u=x+y,v=xy,求dz/dx,dz/dy.
高数题

z=(x+y)^2*cos(x^2*y^2)
dz/dx=2*(x+y)*cos(x^2*y^2)-2*(x+y)^2*sin(x^2*y^2)*x*y^2
dz/dy=2*(x+y)*cos(x^2*y^2)-2*(x+y)^2*sin(x^2*y^2)*x^2*y