Don’t know what this means (Derivative)

Question

I was hoping to get a little help here. :)

I have this equation:

$$\left. \frac{\Bbb d}{\Bbb d\varepsilon} f(\varepsilon) \right|_{\varepsilon =\mu}$$

What I’m not sure about is what the $\varepsilon=\mu$ in the end of the “|” means? Is it just that, in whatever function I have, I just replace $\varepsilon$ with $\mu$?

So if I have like:

$$f(\varepsilon)=\sqrt{\varepsilon }(\varepsilon-u),$$

then I just replace $\varepsilon$ with $\mu$, and in this case I get 0, or does it mean, that I have to take the derivative of the function with respect to $\mu$ and not $\varepsilon$? Or am I totally missing it? :)

Thanks in advance.

Evaluate after differentiation, or any other operations. – Stan Liou Apr 30 '13 at 21:57 — Stan Liou, Apr 30 '13 at 21:57

score 4 · Accepted Answer · answered Apr 30 '13 at 21:58

4

Take the derivative (or whatever operation), then evaluate the result with the condition in the subscript.

answered Apr 30 '13 at 21:58

innisfree

205

score 2 · Answer 2 · edited Dec 07 '23 at 05:07

2

It means “plug in $\mu$ wherever you see $\varepsilon$ after you take the derivative.” In a different notation, it means $f'(\mu)$, where $f'(\varepsilon)=\frac{\Bbb d}{\Bbb d \varepsilon} f(\varepsilon)$.

edited Dec 07 '23 at 05:07

Rócherz

3,976

answered Apr 30 '13 at 22:33

Don’t know what this means (Derivative)

2 Answers2