/sci/ - Science & Math

>>11544516
f(x) is some function F(x) is the area under the graph measured from some fixed end point (you know what I mean). the derivative is by definition
[eqn]F'(x) = \lim \frac{F(x+h)-F(x)}{h}[/eqn]
when h is small, the area F(x+h) - F(x) is approximately a rectangle. therefore this area is the product of the sides of this rectangle. one side is h, the other side is f(x). the fraction in the derivative definition is clearly the formula for the other side. therefore F'(x) = f(x).

I've made some stupid picture.