I'm unsure how the derivative comes out in the following. I have a parametrization $t'=f(t)$ and a parameter $x(f(t))$ and I'm taking: $\frac{d}{d(f(t))}x(f(t))$. I'm not sure if the derivative would come out as $ \frac{df(t)}{dt} \frac{d}{dt}x(t) $ or something else.
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Well, one way to approach this is to use the "fraction" rule $$ \frac{dx}{df} = \frac{dx}{dt} \frac{dt}{df} $$ and here $\frac{dt}{df}$ is the inverse of $\frac{df}{dt}$ – Matti P. Sep 18 '19 at 09:16
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That's what I was suspecting. I have another term which is (df/dt)^-1 which I would have wanted the dx/df to cancel out. – Linus Sep 18 '19 at 09:30