About the Derivative Calculator

Differentiation finds how fast a function changes. The power rule — d/dx(a·xⁿ) = a·n·xⁿ⁻¹ — is applied to every term exactly: 3x² becomes 6x, 2x becomes 2, and constants drop away. Because each term is handled symbolically, the derivative shown is exact, not an approximation.

The Tangent Line

At a point x₀, the derivative equals the slope of the tangent line y = f′(x₀)(x − x₀) + f(x₀). The chart draws both the curve and its tangent across a window around x₀, showing the line that best approximates the curve locally.