If z=(x+y)ey and x=u2+v2 and y=u2−v2, find the following partial derivatives using the chain rule. Enter your answers as functions of u and v. ∂z/∂u=
∂z/∂v=

Step-by-step explanation:

Given the functions  z=(x+y) and x=u²+v² and y=u²−v²

Using the composite derivative formula;

∂z/∂u= ∂z/∂x*∂x/∂u+∂z/∂y*∂y/∂u

∂z/∂u = y*2u + [(x+y)+x]*2u

∂z/∂u =y*2u + 2u[x+y+x]

∂z/∂u = y*2u + 2u[2x+y]

∂z/∂u = 2u[u²−v²]+ 2u[2(u²+v²)+y]]

∂z/∂v= ∂z/∂x*∂x/∂v+∂z/∂y*∂y/∂v

∂z/∂v = y*2v + [(x+y)+x]*-2v

∂z/∂v =y*2v -2v[x+y+x]

∂z/∂v = y*2v -2v[2x+y]

∂z/∂v = 2v[u²−v²]-2v[2(u²+v²)+y]

rx and sx

step-by-step explanation:

step-by-step explanation: