Derivative (mathematics)

In mathematics (particularly in differential calculus), the derivative is a way to show how steep a function is at a given point. Derivatives are similar to the slope of a line, but can be used for other curves as well. It is sometimes called the "instantaneous rate of change" of a function.

More specifically, the derivative is how much a function is changing at one given point. For functions that act on the real numbers, it is the slope of the tangent line at a point on a graph. The derivative is often written as ${\displaystyle {\tfrac {dy}{dx}}}$ ("dy over dx" or "dy upon dx", meaning the difference in y divided by the difference in x). The d is not a variable, and therefore cannot be cancelled out. Another common notation is ${\displaystyle f'(x)}$—the derivative of function ${\displaystyle f}$ at point ${\displaystyle x}$, usually read as "${\displaystyle f}$ prime of ${\displaystyle x}$".^[1][2][3]

1. ↑ "List of Calculus and Analysis Symbols". Math Vault. 2020-05-11. Retrieved 2020-09-15.
2. ↑ Weisstein, Eric W. "Derivative". mathworld.wolfram.com. Retrieved 2020-09-15.
3. ↑ "The meaning of the derivative - An approach to calculus". themathpage.com. Retrieved 2020-09-15.