suppose z=f(x,y) is a differentiable function on R^2 and x=rcos(theta) and y=rsin(theta). compute the partial of z with respect to r.

Question

dumbcow · Answer

what is f(x,y)?

anonymous · Answer

according to the question it can be anything.

anonymous · Answer

damn. is this calc 2?

dumbcow · Answer

dx/dr = cos(theta)
dy/dr = sin(theta)

anonymous · Answer

calc 3

dumbcow · Answer

hmm
say z = x+y
then
dz/dr = cos(theta) + sin(theta)
i think, dang i have forgotten a lot of calc 3

anonymous · Answer

lol. im in calc 1 :D cant rly help you

dumbcow · Answer

$$\frac{dz}{dr} = \frac{dz}{dx}\frac{dx}{dr} + \frac{dz}{dy}\frac{dy}{dr}$$

anonymous · Answer

that's what I was thinking. that's the answer i have. do you have a link or something to that? i'll need that again for future reference.

dumbcow · Answer

no that i actually remembered
i tried looking it up but no luck yet...

anonymous · Answer

i know i've seen that somewhere myself. it was a vague memory but since you thought of the same thing i feel a lot better about it.

anonymous · Answer

I agree with you guys it's called the total derivative. http://en.wikipedia.org/wiki/Total_derivative. The case you are interested in is a little bit down the page

anonymous · Answer

thanks for the link. i feel much better now that two others agree.

dumbcow · Answer

thank you

anonymous · Answer

can either of you help with lagrange multipliers?

anonymous · Answer

for some reason my calc teachers never mentioned them.

anonymous · Answer

what's the problem though I'll try to look it up and maybe I can help?

anonymous · Answer

just posted it