## Abhisar one year ago Can some body make me understand this? $\frac{d T}{d (1/T)} = \frac{1}{\left(\frac{d (1/T)}{d T}\right)}$ How?

1. Abhisar

@ganeshie8 @myininaya

2. Elsa213

@Hero

3. myininaya

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

4. myininaya

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

5. myininaya

6. Abhisar

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

7. Abhisar

Have you used chain rule or something?

8. myininaya

yes I used chain rule above

9. Abhisar

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

10. myininaya

well I did introduce a new function

11. myininaya

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

12. Abhisar

Yes.

13. Abhisar

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

14. Abhisar

Thanks a bunch c:

15. myininaya

np