### 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

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/sec^{2}.