# Partial derivative difference question

1. Mar 17, 2008

### tony873004

What's the difference between $$\partial ^2 x$$ and $$\partial x^2$$?

Is $$\partial ^2 x$$ the same as $$\left( {\partial x} \right)^2$$ like $$\sin ^2 x$$ is the same as $$\left( {\sin x} \right)^2$$?

Thanks!

Last edited by a moderator: Apr 10, 2017
2. Mar 17, 2008

### hotcommodity

If you have $$\frac{\partial^2 x}{\partial t^2}$$, this translates to $$\frac{\partial}{\partial t} \frac{\partial x}{\partial t}$$. In other words, in derivative notation, it's common to write $$\partial t * \partial t$$ as $$\partial t^2$$. Does that help?

3. Mar 17, 2008

### tony873004

so does it mean the second partial derivative, rather than squaring something?

4. Mar 17, 2008

### hotcommodity

In the case of $$\frac{\partial^2 x}{\partial t^2}$$, it means the second partial derivative of a function x with respect to t. You can think of the "partial" terms as being squared, but I'm not sure how that would be of any help unless you're having to separate something like $$\frac{\partial^2 x}{\partial t^2}$$, as was done above. Is there a particular problem that's troubling you?

5. Mar 18, 2008

### tony873004

Yes, this is a small part of a larger problem. But I think I can get it now that I understand the notation. If I get stuck, I'll post the entire problem. Thanks!