## Writing derivatives using the Leibniz notation

All of these are the different ways to write the derivative of a function.

# The derivative of

*constant* function

The derivative equals 0 since there’s no change from one `x`

value to any other `x`

values. It means that there’s no **slope**.

*linear* function

The derivative normally equals 1. `y`

changes by the same amount for every change of `x`

.

The derivative of a linear function equals to the slope `m`

(i.e. `m = 2`

).

*quadratic* function

At any point `x`

, the slope of the tangent line will be `6x`

.

*quadratic* function with addition

### multi-dimensional function

Remember, the derivative of a constant is always 0.