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# total differentiation watch

1. I have this equation:

Where u is a function, ct and cnt are variables and ubar a constant.
And need to find:
Attachment 726832
How would I start this?
2. (Original post by DQd)
I have this equation:

Where u is a function, ct and cnt are variables and ubar a constant.
And need to find:
Attachment 726832
How would I start this?
Just differentiate through by . This means that for the first term you must use the chain rule.
3. I don't like the look of that equation...
4. (Original post by RDKGames)
Just differentiate through by . This means that for the first term you must use the chain rule.
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)?
5. (Original post by DQd)
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 w.r.t , you'd say and not .

If was constant, then yes the derivative would make it 0
6. (Original post by Notnek)
I don't like the look of that equation...
What's wrong with it?
7. (Original post by RDKGames)
Yes that's incorrect.

If you were to differentiate w.r.t , you'd say and not .

If was constant, then yes the derivative would make it 0
Got it.
The solutions only have one step:

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

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
9. (Original post by RDKGames)
What's wrong with it?
Ignore me.

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