Calxsolver
Subject:  Calculus

Derivative

The instantaneous rate of change of a function at a point.

The derivative f'(a) measures how fast f(x) is changing at x = a, defined as the limit of the average rate of change over an interval shrinking to zero. Geometrically it is the slope of the tangent line to the graph at that point.

Formula

f'(a) = lim h→0 (f(a + h) − f(a)) / h

Used in

Polynomial Derivative Differentiate a polynomial exactly with the power rule. Derivative at a Point Numeric derivative of any function of x at a point. Tangent Line Calculator Equation of the tangent line to a curve at a point.

See also

Limit The value a function approaches as the input gets arbitrarily close to a point. Integral The accumulation of a function — the signed area under its graph between two points. Tangent line The line that touches a curve at a point and has the same slope as the curve there.