IN DESPERATE NEED OF HELP!!! - partial derivatives!!

[Sarahisme]

Hi all, i am having real difficulty doing this partial deriv. problem!

 

would anyone be able to help me?

 

(i am not even sure where to start really! )

 

Thanks

 

Sarah

[Sarahisme]

well this is what i have done so far, but i don't really know what i am doing...

 

z = f(x,y) and [math] r = \sqrt(x^2 + y^2) \implies y = \sqrt(r^2 - x^2)[/math]

 

so

 

z = [math] f(x, (r^2 - x^2)^{0.5})[/math]

 

so [math] \frac{\partial z}{\partial x}|_r = \frac{\partial z}{\partial x} \frac{\partial x}{\partial x} + \frac{\partial z}{\partial y} \frac{\partial }{\partial x}(r^2 - x^2)^{0.5} [/math]

 

[math] = \frac{\partial z}{\partial x} - \frac{\partial z}{\partial y} \frac{x}{(r^2 - x^2)^{0.5}}[/math]

 

but yeah... now i'm stuck

[Sarahisme]

ok, wait i think i've got the first bit, but not the second bit of the question (adding the two)

[Sarahisme]

got it all now!