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total differentiation

I have this equation:
Capture.PNG
Where u is a function, ct and cnt are variables and ubar a constant.
And need to find:
Attachment not found

How would I start this?
(edited 6 years ago)
Original post by DQd
I have this equation:
Capture.PNG
Where u is a function, ct and cnt are variables and ubar a constant.
And need to find:
Attachment not found

How would I start this?


Just differentiate through by cntc_{nt}. This means that for the first term you must use the chain rule.
Reply 2
I don't like the look of that equation...
Reply 3
Original post by RDKGames
Just differentiate through by cntc_{nt}. This means that for the first term you must use the chain rule.


Thanks, got the answer.
Didn't think to split the first term.
As an aside, is it incorrect to say the first term Capturetr.PNG is equal to 0 because there is no cnt in 0.5u(ct)?
Original post by DQd
Thanks, got the answer.
Didn't think to split the first term.
As an aside, is it incorrect to say the first term is equal to 0 because there is no cnt in 0.5u(ct)?


Yes that's incorrect.

If you were to differentiate y2=xy^2=x w.r.t xx, you'd say 2ydydx=12y\dfrac{dy}{dx} = 1 and not 0=10 = 1.

If u(ct)u(c_t) was constant, then yes the derivative would make it 0
Original post by Notnek
I don't like the look of that equation...


What's wrong with it?
Reply 6
Original post by RDKGames
Yes that's incorrect.

If you were to differentiate y2=xy^2=x w.r.t xx, you'd say 2ydydx=12y\dfrac{dy}{dx} = 1 and not 0=10 = 1.

If u(ct)u(c_t) was constant, then yes the derivative would make it 0


Got it.
The solutions only have one step:
Captureh.PNG
Is there any slightly different method to solve this or do you think it's just the method you stated but multiplied by dcnt
Original post by DQd
Got it.
The solutions only have one step:
Captureh.PNG
Is there any slightly different method to solve this or do you think it's just the method you stated but multiplied by dcnt


Yes, indeed it is the exact same method as I said but they made an extra step afterwards of multiplying through by dcntd{c_{nt}}
Reply 8
Original post by RDKGames
What's wrong with it?

Ignore me.

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