- #1

- 807

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## Homework Statement

The equations xu^2 + yv = 2, 2yv^2 + xu = 3 define u(x,y) and v(x,y) in terms of x and y near the point (x,y) = (1,1) and (u,v) = (1,1).

Compute the following partial derivatives:

(A) ∂u/∂x(1,1)

(B) ∂u/∂y(1,1)

(C) ∂v/∂x(1,1)

(D) ∂v/∂y(1,1)

The answers are:

(A) ∂u/∂x(1,1) = -0.428571428571429

(B) ∂u/∂y(1,1) = -0.285714285714286

(C) ∂v/∂x(1,1) = -0.142857142857143

(D) ∂v/∂y(1,1) = -0.428571428571429

## Homework Equations

To my knowledge: partial differentiation and implicit differentiation.

## The Attempt at a Solution

I tried implicitly and partially differentiating xu^2 + yv = 2 and got:

u^2 + 2xu∂u/∂x = 0

∂u/∂x = -u^2 /(2xu)

∂u/∂x(1,1) = -(1)^2/(2*1*1) = -1/2 (which is close to the answer but not good enough).

Could someone please tell me what I am doing wrong and how to do this correctly?

Any help would be greatly appreciated!

Thanks in advance!