The derivative is often described as the instantaneous rate of change, the ratio of the instantaneous change in the dependent variable to that of the independent variable. [1] The …

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

Result: the derivative of x3 is 3x2 ... f’ (x) = lim Δx→0 f (x+Δx) − f (x) Δx ... dy dx = f (x+dx) − f (x) dx

Dec 12, 2025 · Derivative, in mathematics, the rate of change of a function with respect to a variable. Geometrically, the derivative of a function can be interpreted as the slope of the …

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.

Dec 29, 2025 · Complete beginner's guide to understanding derivatives in calculus. Learn what derivatives are, how to calculate them, derivative rules, examples, and real-world applications. …

Just like a slope tells us the direction a line is going, a derivative value tells us the direction a curve is going at a particular spot. At each point on the graph, the derivative value is the slope …

For a function to have a derivative at a given point, it must be continuous at that point. A function that is discontinuous at a point has no slope at that point, and therefore no derivative.

Free Derivative Calculator helps you solve first-order and higher-order derivatives. For trigonometric, logarithmic, exponential, polynomial expressions. Answers, graphs, alternate …

Derivative definition The derivative of a function is the ratio of the difference of function value f (x) at points x+Δx and x with Δx, when Δx is infinitesimally small.