One of the first things you'll learn in Calculus is how to differentiate a polynomial. Basically what's going on is you're taking a polynomial and making a function to show its slope. For example:

```+-----------------------------------------------------------------+
|                                |            ##                  | 2.0000
|                                |           ##                   | 1.8000
|                                |           #                    | 1.6000
|                                |          ##                    | 1.4000
|                                |          #                     | 1.2000
|                                |         #                      | 1.0000
|                                |        ##                      | .80000
|                                |        #                       | .60000
|                                |      ##                        | .40000
|                                |    ##                          | .20000
|----------------------------#########----------------------------| .00000
|                          ##    |                                | -.2000
|                        ##      |                                | -.4000
|                       #        |                                | -.6000
|                      ##        |                                | -.8000
|                      #         |                                | -1.000
|                     #          |                                | -1.200
|                    ##          |                                | -1.400
|                    #           |                                | -1.600
|                   ##           |                                | -1.800
|                   #            |                                | -2.000
+-----------------------------------------------------------------+
^-3.095 ^-2.321 ^-1.547 ^-.7738 ^.00000 ^.77380 ^1.5476 ^2.3214 ^3.0952
```

This is the function x3

```+-----------------------------------------------------------------+
|                                |        #                       | 2.0000
|                        #       |       #                        | 1.8000
|                         #      |      ##                        | 1.6000
|                         #      |      #                         | 1.4000
|                          #     |     ##                         | 1.2000
|                          #     |     #                          | 1.0000
|                           #    |    #                           | .80000
|                            #   |   ##                           | .60000
|                            #   |   #                            | .40000
|                             ## | ##                             | .20000
|-------------------------------###-------------------------------| .00000
|                                |                                | -.2000
|                                |                                | -.4000
|                                |                                | -.6000
|                                |                                | -.8000
|                                |                                | -1.000
|                                |                                | -1.200
|                                |                                | -1.400
|                                |                                | -1.600
|                                |                                | -1.800
|                                |                                | -2.000
+-----------------------------------------------------------------+
^-3.095 ^-2.321 ^-1.547 ^-.7738 ^.00000 ^.77380 ^1.5476 ^2.3214 ^3.0952
```

And this function (3x2, called the derivative of x3) shows the slope of x3. In places where x3 is increasing, the derivative (the slope) is positive. In places where x3 is decreasing, the derivative is negative.

So we write:

(d/dx) x3 = 3x2

d/dx stands for "the derivative with respect to x," meaning that x is the independent variable. The above equation could be read "the derivative of x3 is 3x2"

So how do you figure out what the derivative for a given function is? Well, first of all, the derivative of any constant is 0. The derivatives of 1, 2, 500, and 3,000,000 are all 0. This is because if you make a graph of a constant, you get a straight horizontal line, with a slope of 0.

Next, we have the power rule, written thus: (d/dx) xn = nxn-1. So if you have x to any power, just multiply it by that power and subtract 1 from the exponent to get the derivative. For example, (d/dx) x5 = 5x4. If you have a coefficient, just leave it there. Like this: (d/dx) 3x5 = 3 * 5x4 = 15x4.

Just one more rule now: the sum rule. To put it in words, if you have multiple terms in your polynomial, just add up the derivatives. Like this:

(d/dx) (5x2 + 6x3) = (d/dx) 5x2 + (d/dx) 6x3 = 5*2x + 6*3x2 = 10x + 18x2

Hopefully I was relatively clear. My intention in writing this was not to impart a thorough knowledge of Calculus, but just to describe the relatively simple procedure of differentiating a polynomial.