What is a Derivative?

The derivative is an equation for finding the instantaneous rate of change (slope,the m )of a function. This is not the first time in your math career that you have found a rate of change (slope,the m ). In algebra you were finding the rate of change of a line every time you found the slope of a line or were asked to find the average rate of change between two points. The tool you used in algebra to find the average rate of change was the slope equation , $\frac{y_2–y_1}{x_2–x_1}$ . The big difference between the two rates of change is that in calculus we are finding an instantaneous rate of change, the slope at a single point, and in algebra it was an average rate of change, the slope between two points.