# Thread: [SOLVED] Using chain rule to find partial derivative?

1. ## [SOLVED] Using chain rule to find partial derivative?

Hello =)

Suppose that f(x,y) is a function of two variables with
fx (0,2) = 2 and fy (0,2) = -1
Using the chain rule, compute the numeral value of f theta ( r cos theta, r sin theta)
at r = 2, theta = pi/2

I know that if you sub the values of r and theta into f (with respect to theta, given above), you get the point (0,2).

I don't know how to make the connection, and therefore get the answer!

2. If you have a multi-variable function $f(x,y)$, the chain rule looks like this:

$\frac{\partial f}{\partial k} = \frac{\partial f}{\partial x} \, \frac{\partial x}{\partial k} + \frac{\partial f}{\partial y} \, \frac{\partial y}{\partial k}$

Notice that this looks sort of like the single-variable chain rule, except we have to go through both $x$ and $y$ and add it together. In this problem, you want to find $\frac{\partial f}{\partial \theta}$, which means our equation will be:

$\frac{\partial f}{\partial \theta} = \frac{\partial f}{\partial x} \, \frac{\partial x}{\partial \theta} + \frac{\partial f}{\partial y} \, \frac{\partial y}{\partial \theta}$

Can you figure this out from here? Where are you getting stuck?

3. Oh!
I did it just then and I got -4. It seems about right (I don't have the answers/sln for it).
Thanks!!

4. Yes that is the correct answer!