Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Derivative

Revision as of 19:16, 30 July 2006 by Joml88 (talk | contribs) (→‎Notation)

The derivative of a function is defined as the instantaneous rate of change of the function with respect to one of the variables.

Notation

The following are commonly recognized notations for expressing the derivative of a function.

Euler's notation
First derivative $D_xf(x)$ or $Du$
Second derivative $D_x^2f(x)$ or $D^2u$
Third derivative $D_x^3f(x)$ or $D^3u$
$n$th derivative $D_x^nf(x)$ or $D^nu$
Lagrange's notation
First derivative $f'(x)$
Second derivative $f''(x)$
Third derivative $f'''(x)$
$n$th derivative $f^{(n)}(x)$
Leibniz's notation
First derivative $\frac{dy}{dx}$
Second derivative $\frac{d^2y}{dx^2}$
$n$th derivative $\frac{d^ny}{dx^n}$
Newton's notation
First derivative $\dot{x}$
Second derivative $\ddot{x}$

See also

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=Derivative&oldid=8877"