# Partial derivative question

by tony873004
Tags: derivative, partial
 Sci Advisor PF Gold P: 1,544 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! 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution
 P: 436 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?
 P: 436 Partial derivative question 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?