let z=f(x,y) be a differentiable function of two variables. Suppose x= u^2 - v^2 and y = 2u +3v.

Draw a tree diagram relating the variables, then find δz/δu and δz/δv in terms of δf/δx and δf/δy ?

Question

let z=f(x,y) be a differentiable function of two variables. Suppose x= u^2 - v^2 and y = 2u +3v.

Draw a tree diagram relating the variables, then find δz/δu and δz/δv in terms of δf/δx and δf/δy ?

anonymous · Answer

Give me just one second and I'll help you :)

anonymous · Answer

okay thanks! :)

amistre64 · Answer

chain rule again dabears?

anonymous · Answer

Okay, to find dz/du you must use the chain rule. In other words, you realize that z is NOT explicitly in terms of u or v but both. So the chain rule says:$$dz/du=(dz/dx)/(du/dx)$$ Amistre can take it from here :P

anonymous · Answer

okay

amistre64 · Answer

$${dz\over du}={}$$ ..... that did it lol

anonymous · Answer

:D

amistre64 · Answer

Draw a tree diagram relating the variables, then find δz/δu and δz/δv in terms of δf/δx and δf/δy

not sure if you really need a tree diagram drawn up; it just shows the position of the functions

amistre64 · Answer

z = x(u,v) + y(u,v) right?

x= u^2 - v^2      y = 2u +3v

dx/du = 2u     dy/du = 2
dx/dv = -2v    dy/dv = 3

amistre64 · Answer

dz/dx = 2u-2v        dz/dy = 5

amistre64 · Answer

you agree with these?  cause i could be wrong  :)

anonymous · Answer

They look good to me :)

anonymous · Answer

yes, they all make better sense now. I don't understand why the chain rule throws me for a loop each time

anonymous · Answer

bears did you get my answer to the other one?

anonymous · Answer

yes, thank you