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Given a function $c(r)$, where $r \in [0,1]$ and another function

$ x = \alpha \times c(0) $

where $\alpha$ is a constant and $c(0)$ is the function $c$ evaluated at $r = 0$, my question is - what is $\frac{dx}{dc}?$

As $c(r)$ varies, $c(0)$ will vary as well and so I assume the answer is $\frac{dx}{dc}$= $\alpha \frac{d c(0)}{d c}$. But if so, how do I evaluate $\frac{d c(0)}{d c}$?

Thanks!

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    Oops, I missed a point: In the case where $f(c) = c(0)$, since $f$ is linear, the derivative is the same as the function itself, so $c$ doesn't show up anywhere. If the function was not linear, for example $f(c) = c(0)^2$, then the derivative at $c$ would be $g(h) = 2c(0)h(0)$.2012-08-27

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