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    • Thread Starter

    Hi there,
    Could someone with a bit of skill help me differentiate this:

    with respect to RHmeas?

    It's been so long since I did anything like this!

    RHTarget is a constant, RHmeas is a variable, Gmeas is a variable, Gcorr will also be a variable.
    • PS Helper

    PS Helper
    It would probably help visually if you replaced some of the variable names by single letters.

    Let y = g_{\text{corr}}, a = g_{\text{meas}}, x = RH_{\text{meas}}, b = RH_{\text{target}}, then you have

    y = \left( 1 + (a^3 - 1)\dfrac{b}{1-b} \dfrac{1 - x}{x} \right)^{\frac{1}{3}}

    Where I imagine you're holding a,b constant, so now you're trying to find \frac{dy}{dx}. Now it's fairly straightforward. Setting u = 1 + (a^3 - 1)\dfrac{b}{1-b} \dfrac{1 - x}{x} we get \frac{du}{dx} = -(a^3 - 1)\dfrac{b}{1-b}\dfrac{1}{x^2}, and since y = u^{1/3} you can find \frac{dy}{du} fairly easily... then you multiply them together.
    • Thread Starter

    Hello nuodai,

    You're certainly right about swapping variable names for letters!

    If I have y = g_{\text{corr}}, a = g_{\text{meas}}, x = RH_{\text{meas}}, b = RH_{\text{target}}, everything does indeed become simpler.

    Thank you so much for your reply, I am working through it now.

    EDIT: I'll have to use chain rule
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Updated: February 8, 2010

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