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Let say you have a function f that depends on 3 variables: $x,y, t$ and you want to calculate $\dfrac{df(x,y,t)}{dt}$.

In fact you know that $t = c \alpha$ with $c$ a constant and $\alpha$ a variable. So in fact, the function $f$ depends on the variables $(x,y,\alpha)$. How can we calculate $\dfrac{df(x,y,t)}{dt}$ ?

I would think we can do: $\dfrac{df(x,y,\alpha)}{d\alpha} \dfrac{d\alpha}{dt} = \dfrac{df(x,y,\alpha)}{d\alpha} \left(\dfrac{dt}{d\alpha}\right)^{-1} = \dfrac{df(x,y,\alpha)}{d\alpha} \dfrac{1}{c} $ I doubt if this is correct or not.

thanks in advance

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    Yup it seems pretty fine to me. – 2017-01-12
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    Not correct if $x$ or $y$ might depend on $\alpha$. – 2017-01-12
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    @ Open Ball : In my particular case, $x$ and $y$ do not depend on $\alpha$. Do you think it is correct if $x$ and $y$ do not depend on $\alpha$ ? – 2017-01-12
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    Yes, it is correct. – 2017-01-12

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