Calculus is the mathematics of change — so you need to know how to find the derivative of a parabola, which is a curve with a constantly changing slope.
![image0.png](https://www.dummies.com/wp-content/uploads/202363.image0.png)
The figure below shows the graph of the above parabola.
![image1.jpg](https://www.dummies.com/wp-content/uploads/202364.image1.jpg)
Notice how the parabola gets steeper and steeper as you go to the right. You can see from the graph that at the point (2, 1), the slope is 1; at (4, 4), the slope is 2; at (6, 9), the slope is 3, and so on.
![image2.png](https://www.dummies.com/wp-content/uploads/202365.image2.png)
x (horizontal position) | 1 | 2 | 3 | 4 | 5 | 6 | etc. |
y (height) | 0.25 | 1 | 2.25 | 4 | 6.25 | 9 | etc. |
1/2 x (slope) | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 | etc. |
Here’s the calculus. You write
![image3.png](https://www.dummies.com/wp-content/uploads/202366.image3.png)
And you say,
![image4.png](https://www.dummies.com/wp-content/uploads/202367.image4.png)
Or you can say,
![image5.png](https://www.dummies.com/wp-content/uploads/202368.image5.png)
Take the power and put it in front of the coefficient.
Multiply.
(Note that this is only a temporary, interim result on the road to the solution below; by itself, it is meaningless.)
Reduce the power by 1.
In this example, the 2 becomes a 1. So the derivative is