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# Derivatives

Constant - ex: 40.

![](/files/-LfQNVuqtJHTw6LMWNot)

Calculu's job is:

![](/files/-LfQOFEYhifABG2I2Fw1)

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.

![](/files/-LfQSEG-kXYBMWpBDXJj)

### Big Picture Derivatives

![](/files/-LfbU46lv9JQtrPJgqjZ)

![](/files/-LfbU_DmyBJQnkDxuOel)

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. 

![](/files/-LfbVAfe2EP-u7ahle0K)

Therefore dy/dx = 2x. 

So now let's draw the slope: 

![](/files/-LfbVgP4Pg79XlA4bXVk)

Another example: 

![](/files/-LfbVwNr6JPKUxET7iEp)