AI Math SolverA derivative measures a function's instantaneous rate of change — the slope of its tangent line. Learn the concept, notation, and the core rules for computing one.
Solve it with the AI Math SolverThe derivative f′(x) captures how steeply f rises or falls at each point. Physically, it is velocity when f is position; geometrically, it is the slope of the tangent line.
A handful of rules differentiate most functions: the power rule, the product and quotient rules for combinations, and the chain rule for nested functions. Each reuses the limit definition in a shortcut form.
A derivative measures how a function's output changes as its input changes — the slope of the tangent line, or the instantaneous rate of change at a point.
The power rule is the most common: the derivative of xⁿ is n·xⁿ⁻¹. Constants multiply through and the exponent drops by one.