Question

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

Answer 1

@ganeshie8 @myininaya

Answer 2

@Hero

Answer 3

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

Answer 4

\[\frac{1}{\frac{d(\frac{1}{T})}{dT}}=\frac{dT}{d(\frac{1}{T})} \text{ since the reciprocal of } \frac{d(\frac{1}{T})}{dT} \text{ is } \frac{dT}{d(\frac{1}{T})}\]

Answer 5

wait what do you want to understand about this?

Answer 6

Like how can you write \[\frac{d T}{d (1/T)}~as~\frac{1}{\left(\frac{d (1/T)}{d T}\right)} \]

Answer 7

Have you used chain rule or something?

Answer 8

yes I used chain rule above

Answer 9

Umm..But I thought chain rule is used when we differentiate a function with respect to different function. Right?

Answer 10

well I did introduce a new function

Answer 11

would you agree that:
\[\frac{a}{b}=\frac{1}{\frac{b}{a}}?\]

Answer 12

Yes.

Answer 13

Whoops!!!!!!!

lol, I was thinking it to be some complex stuff.

Answer 14

Thanks a bunch c:

Answer 15

np