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Math Help - [SOLVED] Using chain rule to find partial derivative?

  1. #1
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    Red face [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!

    thanks in advance =)
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  2. #2
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    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?
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  3. #3
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    Oh!
    I did it just then and I got -4. It seems about right (I don't have the answers/sln for it).
    Thanks!!
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  4. #4
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    Yes that is the correct answer!
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