Abhisar
  • Abhisar
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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katieb
  • katieb
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Abhisar
  • Abhisar
@ganeshie8 @myininaya
Elsa213
  • Elsa213
@Hero
myininaya
  • myininaya
\[\frac{dT}{d(\frac{1}{T})} \\ \text{ \let } u=\frac{1}{T} \text{ then } T=\frac{1}{u} \\ \text{ so } \frac{dT}{d(\frac{1}{T})} =\frac{d(\frac{1}{u})}{du} \cdot \frac{du}{dT}\]

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

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