Derivatives is a concept introduced in Calculus where it is the instantaneous rate of change or slope at a given point. The slope of a line can be found by or or .

In the linear equation of , the slope is `2`

because for each incremental change of `x`

the output value would be `2`

.

For curves such as a quadratic, the idea of a slope still applies and it is instead called the derivative. has a derivative of `2x`

because for a change in `x`

such as `2`

, the resulting output of the function `g(2)`

is twice the input or in this case `4`

. . . . We say the instantaneous rate of change or the derivative is `2x`

. Instead of saying the whole equation’s slope is `2x`

as we did for `f(x)`

above, we can use the Leibniz notation.

Further reading: Derivatives Wikipedia