Derivatives

Constant - ex: 40.

Calculu's job is:

Given one of those functions, find the other. From function 1 to 2, that is called differential calculus. Going from 2 to 1 (take the speed and understanding what is the distances), that is called integral calculus.

Big Picture Derivatives

Delta y is the difference between the heigh at point x and the height at point x + delta X.

After simplifiying we get y'=2x+Deltax. But Delta x tends toward 0 because in the derivative we want smaller and smaller numbers.

Therefore dy/dx = 2x.

So now let's draw the slope:

Another example: