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Math Help - Gradient of function of functions

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    Gradient of function of functions

    if we have functions f and g, and we let h:=sqrt((f^2) + (e^-fg)) calculate ∇h in terms of f,g,∇f, ∇g?
    Last edited by CaptainBlack; February 10th 2011 at 08:38 PM. Reason: to give informative thread title
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    I can't read your function for \displaystyle h.

    Is it \displaystyle h = \sqrt{f^2 + e^{-fg}} or \displaystyle h = \sqrt{f^2 + e^{-f}g}?
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    Hi, sorry it's \displaystyle h = \sqrt{f^2 + e^{-fg}}
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    The symbol you use is \nabla which means the gradient vector. Are we to assume these are vector functions? Is so, what is meant by the exponential or the product of two vectors?

    If you simply meant "the derivative" and these are all real valued functions of a single variable, then use the chain rule.
    \frac{\partial h}{\partial f}= \frac{1}{2}\left(f^2+ e^{-fg}\right)^{-1/2}(2f- ge^{-fg}),
    \frac{\partial h}{\partial g}= \frac{1}{2}\left(f^2+ e^{-fg}\right)^{-1/2}(-fe^{-fg})
    and then
    \frac{d h}{d x}= \frac{\partial h}{\partial f}\frac{df}{dx}+ \frac{\partial h}{\partial g}\frac{dg}{dx}
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