Calculus
Derivative Calculator
Differentiate functions symbolically — polynomials, trig, exponential, logarithmic and chain rule — and evaluate f′(x) at a point.
(xⁿ)′ = nxⁿ⁻¹
Also called differentiation calculator · derivative solver
Math · 10 calculators
Calculus Calculators
Derivatives, partial derivatives, definite integrals, limits, Riemann sums and rates of change.
Calculus
Partial Derivative Calculator
Compute partial derivatives ∂f/∂x, ∂f/∂y or ∂f/∂z of multivariable functions symbolically and evaluate them at a point.
∂f/∂x: differentiate with respect to x, t…
Also called partial differentiation · multivariable derivative
Calculus
Integral Calculator
Find antiderivatives (indefinite integrals) of polynomials, trig, exponential and common functions, and optionally a definite integral.
∫xⁿ dx = xⁿ⁺¹/(n+1) + C
Also called antiderivative calculator · indefinite integral
Calculus
Definite Integral Calculator
Evaluate definite integrals of any function between two limits using adaptive Simpson integration — area under a curve.
∫ₐᵇ f(x) dx = F(b) − F(a)
Also called area under curve · definite integration
Calculus
Limit Calculator
Evaluate limits of functions as x approaches a value or ±infinity, including one-sided limits and indeterminate forms like 0/0.
lim(x→a) f(x) = L if f(x) gets arbitraril…
Also called limits calculator · find the limit
Calculus
Slope Calculator
Find the slope (gradient) of a line through two points, its angle of inclination, and the line equation y = mx + b.
m = (y₂ − y₁) / (x₂ − x₁)
Also called slope formula · gradient calculator
Calculus
Average Rate of Change Calculator
Find the average rate of change of a function between x = a and x = b — the slope of the secant line.
ARC = (f(b) − f(a)) / (b − a)
Also called rate of change · secant slope
Calculus
Difference Quotient Calculator
Compute the difference quotient (f(x + h) − f(x))/h for a function, and see it approach the derivative as h → 0.
DQ = [f(x + h) − f(x)] / h
Also called difference quotient · f(x+h)-f(x)/h
Calculus
Riemann Sum Calculator
Approximate the area under a curve with left, right, midpoint or trapezoidal Riemann sums, with a table of subintervals.
Σ f(xᵢ*)·Δx, Δx = (b − a)/n
Also called left riemann sum · right riemann sum
Calculus
Numerical Integration Calculator
Compare trapezoidal rule, Simpson's rule and Gauss–Legendre quadrature for any integral, with each method's error.
Trapezoid: h/2·[f₀ + 2f₁ + … + fₙ]
Also called simpson's rule calculator · trapezoid rule calculator
Key calculus formulas
| Derivative | (xⁿ)′ = nxⁿ⁻¹ · (uv)′ = u′v + uv′ · (u/v)′ = (u′v − uv′)/v² · f(g(x))′ = f′(g(x))·g′(x) |
|---|---|
| Partial Derivative | ∂f/∂x: differentiate with respect to x, treating other variables as constants |
| Integral | ∫xⁿ dx = xⁿ⁺¹/(n+1) + C · ∫1/x dx = ln|x| + C · ∫sin(ax) dx = −cos(ax)/a + C |
| Definite Integral | ∫ₐᵇ f(x) dx = F(b) − F(a) |
| Limit | lim(x→a) f(x) = L if f(x) gets arbitrarily close to L as x → a from both sides |
| Slope | m = (y₂ − y₁) / (x₂ − x₁) |
| Average Rate of Change | ARC = (f(b) − f(a)) / (b − a) |
| Difference Quotient | DQ = [f(x + h) − f(x)] / h |
| Riemann Sum | Σ f(xᵢ*)·Δx, Δx = (b − a)/n |
| Numerical Integration | Trapezoid: h/2·[f₀ + 2f₁ + … + fₙ] · Simpson: h/3·[f₀ + 4f₁ + 2f₂ + … + fₙ] |
Calculus questions
Which functions are supported?
Powers and roots, sin, cos, tan, sec, csc, cot, their inverses, sinh, cosh, tanh, exp, ln, log (base 10 or log(x, b)), sqrt, cbrt and abs, combined in any way.
What does the slope mean?
It is the change in y for each 1-unit increase in x — "rise over run". Positive slopes go up to the right, negative slopes go down, 0 is horizontal and vertical lines have undefined slope.