Finding dx & dy: Solving Math Homework Problem

[renlok]

Homework Statement

x = (1/2)(u^2 - v^2), y = uv
find [tex]\delta{x}[/tex] and [tex]\delta{y}[/tex]

Homework Equations

-

The Attempt at a Solution

I think its simple enough but I don't know what sort of method to use to answer this.

Any help would be really awesome :)

 

[p21bass]

With respect to what are you finding the partial derivatives - u or v?

In either case, treat the other variable as a constant. If with respect to u, then treat v as a constant. If with respect to v, then treat u as a constant.

 

[renlok]

not in respect to something i don't need to find a gradient, i need to find the infintesimal change in x or y in terms of v & u.

I've found for finding [tex]\delta{y}[/tex] if you can treat v & u as functions of x you can just use the product rule and divide though by [tex]\delta{x}[/tex] to leave you with [tex]\delta{y} = u\delta{v} + v\delta{u}[/tex]
but I've still no clue how to get [tex]\delta{x}[/tex]

 

[vela]

I'm not sure what you did to find δy. What you said doesn't really make sense. Think of x and y as functions of u and v:

x = x(u,v)
y = y(u,v)

Then you have

[tex]\begin{align*}
dx & = \frac{\partial x}{\partial u} du + \frac{\partial x}{\partial v} dv \\
dy & = \frac{\partial y}{\partial u} du + \frac{\partial y}{\partial v} dv
\end{align*}
[/tex]