# How to read $\frac{d^2y}{dx^2}$

Is it correct to say 'dee squared y over dee x squared'?

I am just trying to make sure because I have to teach this to someone.

I learnt that $$f''(x)$$ is pronounced 'f double prime of x' but I couldn't find how to pronounce Leibniz notation. Thanks!

• I don't think there is any "official" way to read this symbol. I would just call it the second derivative. – user9464 Jan 18 at 0:49
• It's the second derivative indeed – imranfat Jan 18 at 0:49
• The way you pronounce it is fine. That's what I say. – Lee Mosher Jan 18 at 0:52
• I think people often leave out the word "over" – J. W. Tanner Jan 18 at 1:12
• I always say "second derivative" but in my heart I say "dee two y, dee x squared". Have you checked Khan Academy? – Neat Math Jan 18 at 3:04

Three ways of reading $$\dfrac {d^2 y}{dx^2}$$...

1. "dee squared y over dee x squared" (your way)
2. "dee two y over dee x two" (informal)
3. The second derivative of $$y$$ with respect to $$x$$ (formal)
• Did you mean the second derivative of $\color{red}y\,?$ – J. W. Tanner Jan 18 at 1:33
• Saying “squared” between “dee” and “ex” resolves the issue addressed with the asterisk – gen-ℤ ready to perish Jan 18 at 1:42
• Your (1) and (2) are missing a word like "over" or "by" corresponding to the horizontal bar in the fraction. – Rob Arthan Jan 18 at 2:05
• @RobArthan: isn't that word commonly elided? – J. W. Tanner Jan 18 at 2:21
• "dee two y over dee x two" is the best! much more natural. – Bertrand Wittgenstein's Ghost Jan 18 at 3:43

Formally, you should say : second order derivative of y w.r.t. x

I'm pretty sure you read it either

• dee two y by dee x squared

or

• dee two y over dee x squared

(either is fine)

You could read as: "dee two y over dee x two"

• No! $R2D2 \neq R^2D^2$ (put $R =D =1$ to see why not). $\ddot{\smile}$ – Rob Arthan Jan 20 at 0:55

Yes, we read it this way. But it is actually the second derivative of the function $$y$$ which is a function of $$x$$.