In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function 's output with respect to its input. The derivative of a function of a single variable at a …

Jun 13, 2025 · derivative, in mathematics, the rate of change of a function with respect to a variable. Derivatives are fundamental to the solution of problems in calculus and differential …

Geometrically, the derivative is the slope of the line tangent to the curve at a point of interest. It is sometimes referred to as the instantaneous rate of change.

A derivative in calculus is the instantaneous rate of change of a function with respect to another variable. Differentiation is the process of finding the derivative of a function.

Nov 16, 2022 · In this section we define the derivative, give various notations for the derivative and work a few problems illustrating how to use the definition of the derivative to actually …

Jun 24, 2024 · Determine the derivative of f (x) = cos⁡ (x). Choose the correct answer cos (x) −sin (x)

Explore the fundamentals of derivatives, including types, basic rules, 2nd derivative, implicit differentiation, and derivatives of trigonometric and inverse functions.

Differentiation techniques are the methods and rules used to find the derivative of a function. These techniques simplify the process of finding derivatives, especially for complex functions.

The derivative is often written as ("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.

The Derivative Calculator lets you calculate derivatives of functions online — for free! Our calculator allows you to check your solutions to calculus exercises. It helps you practice by …