# Partial derivative difference question

Gold Member
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!

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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?

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

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?