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.