Finding dx & dy: Solving Math Homework Problem

[renlok]

Homework Statement

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

Homework Equations

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

 

[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

$$\begin{align*}<br /> dx & = \frac{\partial x}{\partial u} du + \frac{\partial x}{\partial v} dv \\<br /> dy & = \frac{\partial y}{\partial u} du + \frac{\partial y}{\partial v} dv<br /> \end{align*}$$