Calculus Calculators

Enter a function of x — polynomials, trig, exp, ln — to get f′(x) exactly, and optionally f′(a) at a point, with the supported grammar stated.

Enter a function and a search window to get every critical point in it, classified by the second-derivative test, with f′ and f″ shown and the points plotted.

Enter a function and both bounds to get ∫ₐᵇ f(x)dx, labelled as exact or as a numerical approximation via Simpson's rule.

Enter a function and a point a to get the tangent line y = f(a) + f′(a)(x − a), its slope, and a graph of the curve with the line drawn on it.

Enter a function, the value x approaches and a direction to get the limit — or a clear report that it does not exist — with the numeric approach table.

Enter a function of x — polynomials, trig, exp, ln — to get f′(x) exactly, and optionally f′(a) at a point, with the supported grammar stated.

Enter a function to get f′(x) and f″(x) symbolically, optionally evaluated at a point, with the concavity the second derivative describes.

Enter a function and an order n to get f⁽ⁿ⁾(x) symbolically, with the original function beside it for reference.

Enter a function and a point a to get the tangent line y = f(a) + f′(a)(x − a), its slope, and a graph of the curve with the line drawn on it.

Enter a function of x, y and z, choose the variable, and get ∂f/∂x (or y, z) with the others held constant — optionally evaluated at a point.

Enter f(x, y, z) to get the gradient vector ⟨∂f/∂x, ∂f/∂y, ∂f/∂z⟩ with each component listed separately.

Enter P, Q and R — each a function of x, y and z — to get the scalar divergence ∂P/∂x + ∂Q/∂y + ∂R/∂z.

Enter P, Q and R to get the curl vector via the determinant formula, with its three components listed separately.

Enter f(x) to get ∫f(x)dx + C, or a clear note when the pattern is outside the supported integration grammar.

Enter a function and both bounds to get ∫ₐᵇ f(x)dx, labelled as exact or as a numerical approximation via Simpson's rule.

Enter a function, bounds, a method and an interval count to get the approximation with an error estimate from doubling the intervals.

Enter a function, the value x approaches and a direction to get the limit — or a clear report that it does not exist — with the numeric approach table.

Enter a function, a centre and a number of terms to get the Taylor polynomial and its term list, with exact coefficients f⁽ⁿ⁾(a)/n!.

Enter a function and a number of terms to get its Maclaurin series — the Taylor series about 0 — with the coefficients and term list.

Enter a function and a search window to get every critical point in it, classified by the second-derivative test, with f′ and f″ shown and the points plotted.

Enter a function of x — polynomials, trig, exp, ln — to get f′(x) exactly, and optionally f′(a) at a point, with the supported grammar stated.

Enter a function to get f′(x) and f″(x) symbolically, optionally evaluated at a point, with the concavity the second derivative describes.

Enter a function and an order n to get f⁽ⁿ⁾(x) symbolically, with the original function beside it for reference.

Enter a function and a point a to get the tangent line y = f(a) + f′(a)(x − a), its slope, and a graph of the curve with the line drawn on it.

Enter a function of x, y and z, choose the variable, and get ∂f/∂x (or y, z) with the others held constant — optionally evaluated at a point.

Enter f(x, y, z) to get the gradient vector ⟨∂f/∂x, ∂f/∂y, ∂f/∂z⟩ with each component listed separately.

Enter P, Q and R — each a function of x, y and z — to get the scalar divergence ∂P/∂x + ∂Q/∂y + ∂R/∂z.

Enter P, Q and R to get the curl vector via the determinant formula, with its three components listed separately.

Enter f(x) to get ∫f(x)dx + C, or a clear note when the pattern is outside the supported integration grammar.

Enter a function and both bounds to get ∫ₐᵇ f(x)dx, labelled as exact or as a numerical approximation via Simpson's rule.

Enter a function, bounds, a method and an interval count to get the approximation with an error estimate from doubling the intervals.

Enter a function, the value x approaches and a direction to get the limit — or a clear report that it does not exist — with the numeric approach table.

Enter a function, a centre and a number of terms to get the Taylor polynomial and its term list, with exact coefficients f⁽ⁿ⁾(a)/n!.

Enter a function and a number of terms to get its Maclaurin series — the Taylor series about 0 — with the coefficients and term list.

Enter a function and a search window to get every critical point in it, classified by the second-derivative test, with f′ and f″ shown and the points plotted.