How to notate derivative at a certain point?

Asked Nov 07 '13 at 19:15

Active Nov 07 '13 at 20:12

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I have a simple question.

I have so far always used $f'(x)$ as a derivative notation. For example, if I have a function $y=x^4$ then $y'(x)=4x^3$ and $y'(x)=0$ when $x_1=x_2=x_3=2$. And If I want to find whether $x=0$ is a minima or maxima point then I have done like this: $y''(x)=12x^2$ and $y''(2)=12*2^2=48>0$ so it's the minima point.
Now I have started using $dy/dx$ and everything is fine:
$dy/dx=4x^3$
$dy/dx=0$
$x_1=x_2=x_3=2$
$d^2y/dx^2=12x^2$
But now I'm a bit confused because I don't know how should I note the second derivative at $x=2$ with $dy/dx$. Is it correct to write it like this $dy/d(2)$?

I know that the question might seem a bit dumb but I just would like to know what is the correct notation?

asked Nov 07 '13 at 19:15

SomeOne

the value of the derivative of $y$ at a point $x = a$ can be written as $$\frac{dy}{dx}\left.{!!\frac{}{}}\right|_{x=a} = \frac{dy}{dx}(a)$$ Take a look at http://en.wikipedia.org/wiki/Notation_for_differentiation – Ömer Nov 07 '13 at 19:26
@Ömer Thank you very much! – SomeOne Nov 07 '13 at 19:39
You are welcome. – Ömer Nov 07 '13 at 19:40
there is no minima at $x_1=x_2=x_3=2$ – www.pieronigro.de Nov 07 '13 at 20:12
@LincolnHawk Yes, of course. I made the error by accident. The minima is at $x = 0$. Thanks! – SomeOne Nov 17 '13 at 13:59

How to notate derivative at a certain point?

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