**Random Numbers**, a derivative function is used to calculate the slope of a tangent line on a curve at any given point. You know to calculate the slope of line is basically rise over run? Derivatives are for finding slopes of lines tangent to a curve.

For example, consider the graph f(x) = x^2. It's a curve (a parabola to be specific), so calculating the slope of a tangent line isn't easy. That's where the derivative comes in. Derivatives are evaluated using limits. If I recall correctly, it looks something like this:

f'(a) = lim [f(b) - f(a)] / (b - a)

____{b -> a}

By the way, as a bit of a spoiler, the derivative of the f(x) = x^2 function is 2x, so the slope of a line tangent to it at x = 1.5 would be 3. (You will see this for yourself later, if you haven't already).