Derivative
The definition for the derivative of a function is
Explanation
In general, you can determine the differential quotient of any function that is continuous. In the graphic you can see that the formula is the tangent line to the curve.
If the function y = f (x) is differentiable, you can write it as
or
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These different notations are often used interchangeably. That seems confusing, but in practice it is quite usefull.
The symbol is not a fraction. You read it as d y d x.
Examples
If you drive 30 km on a bicycle in 2 hours, you can calculate the speed as 30 / 2 = 15 km/h.
If you suddenly put the breaks in a car that has a speed of 80 km/h, and you stand still within 10 seconds, you can derive the braking force. Because 80 km/h / 10 sec = 2,2 m/sec2.