Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Is it equal to $\partial ^2 u / \partial x ^2$?

I am trying to figure that out. I don't think it's the case, but I am just trying to make sure.

share|cite|improve this question

$( \partial u / \partial x )^2$ is the derivative squared, while $\partial ^2 u / \partial x ^2$ is the second derivative (that's the notation for 2nd derivative).

share|cite|improve this answer

As others have mentioned, they are not the same. $$ ( \partial u / \partial x )^2 = ( \partial u / \partial x )( \partial u / \partial x ) $$ while $$ \partial^2 u / \partial x^2 = \partial / \partial x(\partial u / \partial x). $$ To show an example. If $u = f(x,y) = x^2y$, then $$ ( \partial u / \partial x )^2 = (2xy)^2 $$ and $$ \partial^2 u / \partial x^2 = \partial / \partial x (2xy) = 2y. $$

share|cite|improve this answer

No, it is just the number $\partial u/\partial x$ multiplied by itself.

There's no simpler way of writing that, as long as you don't know how $u$ is a function of $x$.

share|cite|improve this answer

It's not.

Let $f = \partial u / \partial x $.

Then, $( \partial u / \partial x )^2 = f^2 $ (assuming $f$ returns a number) and $\partial f / \partial x = \partial ^2 u / \partial x ^2$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.