Hi all. I've recently started working a lot on my background in math and physics, since this year I began a new masters program which is quite math/physics heavy and I don't have a formal background in either field. I will try to get active on this forum, since I've been luring for some time and I find it really useful.(adsbygoogle = window.adsbygoogle || []).push({});

Right now I'm going through partial derivatives and some of the questions in the book I'm working with are quite confusing and I'm stuck. Here is one few examples:

z=x[itex]^{2}[/itex]+2y[itex]^{2}[/itex]

x=rcos(θ)

y=rsin(θ)

Question: [itex]\frac{∂^{2}z}{∂y∂θ}[/itex]

Here's what I've done so far:

I took the partial derivative with respect to θ = 2r[itex]^{2}[/itex]cosθsinθ

Now, from here I'm supposed to take the partial of the above with respect to y. I could either express it in terms of x and y:

[itex]\frac{∂2xy}{∂y}[/itex]

or in terms of r and θ:

[itex]\frac{∂2r^{2}sinθcosθ}{∂rsinθ}[/itex]

The thing is that I have no idea how to solve any of the above. The first I don't know how to solve because x and y aren't independent, so I can't just treat x as a constant. I got stuck when I attempted using the chain rule as well. The second I can't solve, since I don't know how to take a partial derivative with respect to a function, rather than a variable.

I would appreciate it if somebody explained how I can solve the problem using both methods (if both are possible, that is).

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# Partial derivative with respect to a function, rather than variable?

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