what is a derivitive?
And how do you get it (f(x)=2x) from f(x)=x^2-3?
Hmmmm. YOu must be only in limits,not yet to derivatives.
If there is a function f(x), the derivative is defined as...
lim d>>0 of (f(x+d) -f(x))/d
Oh! I've seen that equation we just don't call it a derivative. thanks!
This is ahead of your class..
http://en.wikipedia.org/wiki/Derivative
One thing I strongly recommend to you, is go visit the nearest college bookstore, or Barnes Noble, and take a close look at this: Schaum's Outline Series, Calculus.
It is inexpensive, chock full of example problems worked, and is easy to read. Don't hesitate...ask mom for an early birthday present of it.
A derivative is a concept in calculus that measures the rate at which a function is changing at any given point. In simpler terms, it tells you how the function is behaving locally around a specific value of x. It is denoted by the symbol "d/dx" or "f'(x)".
To find the derivative of a function, there are several methods you can use depending on the complexity of the function. In the case of f(x) = x^2 - 3, we can find the derivative using the power rule, which is applicable to functions in the form f(x) = x^n.
Here is the step-by-step process:
1. Start with the original function: f(x) = x^2 - 3.
2. Identify the power to which x is raised. In this case, it's 2.
3. Multiply the coefficient of x by the exponent, which gives you 2x.
4. Subtract 1 from the exponent, which gives you 2 - 1 = 1.
5. Rewrite the result from step 3 as the coefficient of x and rewrite the result from step 4 as the new exponent.
6. The final derivative is f'(x) = 2x.
Therefore, the derivative of f(x) = x^2 - 3 is f'(x) = 2x.