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Math Help - Partial Derivatives

  1. #1
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    Partial Derivatives

    Let h(x,y))= f(\frac{x+y}{x-y}) where f is a C^1 class function.

    Find \frac{dh}{dx} and \frac{dh}{dy}

    I'm having trouble understanding the relationship between the h and f and what functions are contained within each.
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  2. #2
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    Re: Partial Derivatives

    \frac{dh}{dx}\;=\;\frac{dh}{df}\cdot\frac{df}{dx}

    In the old days, back in Calculus I, we called this the chain rule.

    We don't know much about f, so just go with f'. That should do it.
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  3. #3
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    Re: Partial Derivatives

    Well, since this is not Calculus I, those should be partial derivatives: If we let u(x,y)= \frac{x+ y}{x- y},
    \frac{\partial h}{\partial x}= \frac{df}{du}\frac{\partial u}{\partial x}
    \frac{\partial h}{\partial y}= \frac{df}{du}\frac{\partial u}{\partial y}

    Yes, you can write "df/du" as just f '.
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  4. #4
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    Re: Partial Derivatives

    I think I've never coded a "partial" in LaTeX. That's weird. I wonder how I managed to miss that...

    \frac{\partial y}{\partial x}

    Okay, I think I have it, now.
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