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
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