Total derivative with a constraint

  • Thread starter Bman12345
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Hi there,

I have what I suspect is a straightforward question.

I wish to take the total derivative of the following function:

[itex]W(q,x) = q \cdot u(x) + c(q,x)[/itex]

Subject to the constraint: [itex]\frac{q}{x}[/itex]=[itex]\bar{m}[/itex], where [itex]\bar{m}[/itex] is some constant > 0, and c(q,x) is additively separable.

Without the constraint the total derivative is simply:

[itex] dW(q,x) = u(x) dq + q \cdot u_{x} dx + c_{q}(q,x) dq + c_{x}(q,x) dx [/itex]

My question is: How do I incorporate the constraint?

Thanks for any help!

Brent.
 

Answers and Replies

  • #2
mathman
Science Advisor
7,771
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The constraint seems to be q = xm, so dq = mdx.
 

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