The derivative, or rate of change, of a function is another function that gives the value of the slope at every point on the x axis of the original function.  There is more than one way to write the derivative, but we will stick with dy over dx for this exercise. It is fairly simple to find the derivative of simple equations.  First you bring the exponent down and multiply it by the coefficient.  Then you take the previous exponent and subtract that by 1.  This is now the new exponent.  This new function is the derivative. Example: We start of with 3 times x squared.  We bring down the exponent of 2 and multiply that by 3.  We then subtract the exponent, 2, by 1.  The new exponent is now 1.  We now end up with 6x as the derivative. Graph: This is the graph of the function, y = 3x2. Graph: This is the graph of y = 6x.  As you can see this graph follows the slope of y = 3x2.   Where the slope is a big positive number in the graph above, the y in the graph below is a big positive number.  They match up perfectly.