Differentiation and Integration in Calculeaf

Calculus tools sit under Math → Operators ▾ → Calculus: ∫, Σ, Π, lim, d/dx, ∂/∂x, and logs. Click a token to insert the typed function at the caret.

The Math Operators dropdown open on the Calculus category. — Operators ▾ → Calculus. Insert d/dx, ∫, Σ, Π, or lim into the focused math region.

Differentiation

diff(expr, var) (ribbon d/dx) differentiates with respect to a name. pdiff is the partial form (∂/∂x).

diff(x^2, x) =
pdiff(x * y, x) =

The first argument is the expression; the second is the variable. Units on x flow through the derivative the same way they would on paper (a length squared differentiated by a length is a length).

Integration and discrete sums

nintegrate(var, a, b, expr) is a numeric integral. nsum and nprod sum or multiply over a range (ribbon Σ and Π).

nintegrate(x, 0, 1, x^2) =
nsum(i, 1, 10, i) =
nprod(k, 1, 4, k) =

Argument order: index or variable name, start, end, body. Check units on the integrand the same way you would on any other expression — a length in ln() still errors.

Limits

The lim token inserts a limit helper. These are worksheet helpers — not a computer-algebra notebook. If a symbolic form cannot be found, the region shows an error instead of a silent approximation.

Insert a 2D plot or a sweep table when you want a curve or a column of values. Typed names are in the function catalog.