🧮 Free study tool

Derivative Calculator

Enter a function and see the derivative step by step — including the rules applied.

Examples:

Allowed: + − · / ^, brackets, x, e, π plus sin, cos, tan, exp, ln, sqrt. Tip: “2x” and “x^2” work directly.

How does differentiation work?

The derivative of a function describes its instantaneous rate of change — the slope of the graph at every point. This calculator breaks each function into its parts and applies the right rules:

  • Power rule: (xⁿ)′ = n·xⁿ⁻¹
  • Sum rule: Each term is differentiated separately.
  • Product rule: (u·v)′ = u′·v + u·v′
  • Quotient rule: (u/v)′ = (u′·v − u·v′)/v²
  • Chain rule: outer derivative · inner derivative

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