Calculus Calculators
Last updated: September 2026
Chain Rule Derivative Calculator
Evaluates the derivative of a composite polynomial function y = a(bx + c)ⁿ at a given x value using the chain rule.
Critical Points Calculator
Finds the x-coordinate of the critical point (vertex) of a quadratic function ax² + bx + c by setting its derivative equal to zero.
Area Under Curve Calculator
Computes the exact area between a parabola f(x) = ax² + bx + c and the x-axis over an interval [x₁, x₂].
Area Between Curves Calculator
Finds the enclosed area between two power-function curves over a chosen interval.
Numerical Derivative Calculator
Compute the derivative of a power function f(x) = c·x^n + k at a chosen point using either the analytical power rule or a numerical finite-difference approximation.
Optimization Calculator
Find the largest area a rectangle can enclose with a fixed perimeter — a classic quadratic optimization: the area A(x) = x(P/2 − x) peaks at its vertex x = P/4, a square.
Riemann Sum Calculator
Approximate the definite integral of a power function f(x) = c·xⁿ over an interval using left, right, or midpoint Riemann sums.
Tangent Line Calculator
Finds the equation of the tangent line to f(x) = c·xⁿ + k at a specified x-value.
Partial Derivative Calculator
Computes the partial derivative of a two-variable power function f(x,y) = a·xᵐ·yⁿ with respect to either x or y at a specific point.
Implicit Differentiation Calculator
Finds the slope dy/dx of a conic section curve (circle or ellipse) defined by Ax² + By² = C at a specified point.
Surface Area of Revolution Calculator
Calculates the surface area generated when the curve y = ax^n is revolved around the x-axis or y-axis between two bounds.
Rectangular Rule Integration
Approximate a definite integral using a rectangular (midpoint-style) rule with a chosen number of subintervals and an averaged function value.
Arc Length Calculator
Compute the approximate arc length of a curve f(x) between two x-values using a constant average derivative.
Surface of Revolution Calculator
Calculates the surface area formed when a quadratic curve f(x) = c0 + c1·x + c2·x² is rotated around the x-axis or y-axis over a chosen interval.
Chain Rule Calculator
Compute the derivative of a composite function f(g(x)) where f(u) = c·u^n and g(x) = m·x + b, evaluated at a given x.
Definite Integral Calculator
Numerically evaluates the definite integral of a power function ax^n over a specified interval.
Concavity Calculator
Evaluates the second derivative of a cubic f(x) = ax³ + bx² + cx at a test point to determine concavity.
Trapezoidal Rule Calculator
Approximate the definite integral of a function over [a, b] by summing trapezoid areas across n subintervals.
Related Rates Calculator
Compute the rate of area change of a circle whose radius grows at a constant rate, evaluated after a given elapsed time.
Taylor Series Calculator
Approximates the value of common functions (eˣ, sin x, cos x, ln x) using their Taylor series expansion around a chosen center point.
Average Value of Function Calculator
Computes the average value of f(x) = c·xⁿ + k over an interval [a, b].
Limit Calculator
Compute the limit of a rational function (numerator_coeff · x^numerator_power) / (denominator_coeff · x^denominator_power) as x approaches a given value via direct substitution.
First-Order ODE Solver
Solves first-order linear ODEs of the form a·y' + b·y = c with an initial condition y(0).