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Thread: derivative

  1. #1
    Junior Member
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    derivative

    Help me explain the formula:
    "for $\displaystyle f(t,\widetilde{Z}(t))$ we have:
    $\displaystyle df=\frac{df}{dt}[dt]+\frac{df}{dz}[dZ]+\frac{1}{2}\frac{d^2 z}{dz^2}[dt]$
    $\displaystyle \frac{df}{dt},\frac{df}{dz},\frac{d^2f}{dz^2}$ are usual derivatives from calculus."
    Thanks a lot.
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  2. #2
    MHF Contributor

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    Quote Originally Posted by mahefo View Post
    Help me explain the formula:
    "for $\displaystyle f(t,\widetilde{Z}(t))$ we have:
    $\displaystyle df=\frac{df}{dt}[dt]+\frac{df}{dz}[dZ]+\frac{1}{2}\frac{d^2 z}{dz^2}[dt]$
    $\displaystyle \frac{df}{dt},\frac{df}{dz},\frac{d^2f}{dz^2}$ are usual derivatives from calculus."
    Thanks a lot.
    Well, I can't explain it. For one thing, I have no idea what $\displaystyle \frac{d^2 z}{dz^2}$ could mean, if it isn't 0!
    $\displaystyle \frac{dz}{dz}= 1$ so differentiating again gives 0.
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