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Partial derivative question

by tony873004
Tags: derivative, partial
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tony873004
#1
Mar17-08, 08:25 PM
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P: 1,542
What's the difference between [tex]\partial ^2 x[/tex] and [tex]\partial x^2 [/tex]?

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

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
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hotcommodity
#2
Mar17-08, 08:40 PM
P: 436
If you have [tex] \frac{\partial^2 x}{\partial t^2} [/tex], this translates to [tex] \frac{\partial}{\partial t} \frac{\partial x}{\partial t} [/tex]. In other words, in derivative notation, it's common to write [tex] \partial t * \partial t [/tex] as [tex] \partial t^2 [/tex]. Does that help?
tony873004
#3
Mar17-08, 08:46 PM
Sci Advisor
PF Gold
P: 1,542
so does it mean the second partial derivative, rather than squaring something?

hotcommodity
#4
Mar17-08, 08:51 PM
P: 436
Partial derivative question

In the case of [tex] \frac{\partial^2 x}{\partial t^2} [/tex], 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 [tex] \frac{\partial^2 x}{\partial t^2} [/tex], as was done above. Is there a particular problem that's troubling you?
tony873004
#5
Mar18-08, 12:52 AM
Sci Advisor
PF Gold
P: 1,542
Quote Quote by hotcommodity View Post
Is there a particular problem that's troubling you?
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!


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