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Confused on this notation! partial derivatives!

  1. Oct 19, 2005 #1
    Hello everyone I have no idea how to start this problem because i'm confused on the notation, what does it mean?
    here is a picture:
    http://img291.imageshack.us/img291/1177/lastscan2lc.jpg
    I know how to take partial derivatives, but the d^2 part is confusing and the dx^2? what the!
     
  2. jcsd
  3. Oct 19, 2005 #2
    The "d^2/dt^2" part means it is a second order derivative. It basically means how many times you take that derivative.

    So when you have: [tex] \frac{d^1 x^2}{dx^1}[/tex] then this means... take the derivative of x^2 one time. So you get 2x.

    Now if you you had [tex] \frac{d^2 x^2}{dx^2} [/tex] then this means you take the derivative twice. So in TI-89 syntax you would have:

    d(d(x^2,x),x)

    which equals 2.
     
  4. Oct 19, 2005 #3

    TD

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    Homework Helper

    It may be a but confusing at first, but you'll get used to it. Note that the "square" is at the 'd'-sign in the numerator and above the x (or any other variable) in the denominator. Of course, we still mean the variable x, and not x². In the nominator, it still has to be clear that we're differentiating f, and not f².

    So (I'm using normal derivatives here, not partials, but the notation is similar)
    [tex]\frac{{d^2 f}}{{dx^2 }} = \frac{d}{{dx}}\left( {\frac{{df}}{{dx}}} \right)[/tex]

    But watch out, not one of the following:
    [tex]\frac{{df^2 }}
    {{dx^2 }},\frac{{d^2 f}}
    {{d^2 x}},\frac{{df^2 }}
    {{d^2 x}}[/tex]
     
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