Total derivative with a constraint

[Bman12345]

Hi there,

I have what I suspect is a straightforward question.

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

W(q,x) = q \cdot u(x) + c(q,x)

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

Without the constraint the total derivative is simply:

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

My question is: How do I incorporate the constraint?

Thanks for any help!

Brent.

 

[mathman]

The constraint seems to be q = xm, so dq = mdx.