AI Math SolverA derivative calculator differentiates functions and shows each rule. Enter an expression to get its derivative with the power, product, quotient, and chain rules applied step by step.
A derivative measures how a function changes as its input changes — its instantaneous rate of change, or the slope of the tangent line at any point.
The calculator identifies the structure of the function and applies the matching rule. For composite functions it uses the chain rule, multiplying the outer derivative by the inner derivative.
The power rule gives d/dx [xⁿ] = n·xⁿ⁻¹. Constants multiply through and drop by one power; the calculator applies this and the product, quotient, and chain rules as needed.
The derivative of f(x) at a point is the slope of the tangent line there. It measures instantaneous rate of change — velocity is the derivative of position.