Confused on this notation partial derivatives

In summary, the notation "d^2/dx^2" represents a second order derivative, meaning the derivative is taken twice. It is similar to taking the derivative once, but with an added "d" in the numerator and a "dx" in the denominator. It may seem confusing at first, but with practice it will become easier to understand. Just be careful not to confuse it with other notations such as "df^2/dx^2" or "d^2f/d^2x".
  • #1
mr_coffee
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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!
 
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  • #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.
 
  • #3
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]
 

FAQ: Confused on this notation partial derivatives

1. What does the notation "partial derivatives" mean?

The partial derivative is a mathematical concept that represents the rate of change of a function with respect to one of its variables, while keeping all other variables constant.

2. How is the partial derivative notation written?

The partial derivative notation is written as ∂f/∂x, where f is the function and x is the variable with respect to which the derivative is being taken.

3. What is the difference between partial derivatives and regular derivatives?

The main difference between partial derivatives and regular derivatives is that partial derivatives only consider the change in one variable, while regular derivatives consider the change in the entire function.

4. What does "confused on this notation" mean when referring to partial derivatives?

When someone says they are "confused on this notation", it means they are having difficulty understanding or interpreting the symbols and mathematical expressions used in partial derivatives.

5. How are partial derivatives used in science and research?

Partial derivatives are used in various fields of science and research, such as physics, engineering, economics, and more. They are used to analyze and model systems with multiple variables and to find the optimal values of these variables for a given function.

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