Can some body make me understand this? \[\frac{d T}{d (1/T)} = \frac{1}{\left(\frac{d (1/T)}{d T}\right)} \] How?

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Can some body make me understand this? \[\frac{d T}{d (1/T)} = \frac{1}{\left(\frac{d (1/T)}{d T}\right)} \] How?

Mathematics
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\[\frac{dT}{d(\frac{1}{T})} \\ \text{ \let } u=\frac{1}{T} \text{ then } T=\frac{1}{u} \\ \text{ so } \frac{dT}{d(\frac{1}{T})} =\frac{d(\frac{1}{u})}{du} \cdot \frac{du}{dT}\]

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\[\frac{1}{\frac{d(\frac{1}{T})}{dT}}=\frac{dT}{d(\frac{1}{T})} \text{ since the reciprocal of } \frac{d(\frac{1}{T})}{dT} \text{ is } \frac{dT}{d(\frac{1}{T})}\]
wait what do you want to understand about this?
Like how can you write \[\frac{d T}{d (1/T)}~as~\frac{1}{\left(\frac{d (1/T)}{d T}\right)} \]
Have you used chain rule or something?
yes I used chain rule above
Umm..But I thought chain rule is used when we differentiate a function with respect to different function. Right?
well I did introduce a new function
would you agree that: \[\frac{a}{b}=\frac{1}{\frac{b}{a}}?\]
Yes.
Whoops!!!!!!! lol, I was thinking it to be some complex stuff.
Thanks a bunch c:
np

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