Calculus

Derivatives at a point, definite integrals, limits and sums work in every calculator mode, and with units in Physics mode. For a function as a whole (its derivative, antiderivative, zeros and graph) use Curve sketching.

These are easiest to type in the LaTeX source.

Derivative at a point

\left.\frac{d}{dx} (3x^2+1)^4\right|_{x=1}

$$1536$$

The derivative is taken symbolically, then the point is put in. A derivative without a point is an error that tells you how to add one.

Definite integrals

Input	Result
\int_0^{\pi} \sin(x)\,dx	$2$
\int_1^{\infty} \frac{1}{x^2}\,dx	$1$
\int_{-\infty}^{\infty} e^{-x^2}\,dx	$1{,}77245385090551602729816748334$

Integrals are computed numerically, to at most 30 digits; exact values such as $2$ are recognised. The differential can be written dx, d x or \mathrm{d}x. Bounds with units give the integration variable that unit:

\int_0^{2s} 3\frac{m}{s}\,dt

$$6\,\mathrm{m}$$

Limits

Input	Result
\lim_{x \to 0} \frac{\sin x}{x}	$1$
\lim_{x \to \infty} (1+\frac{1}{x})^x	$2{,}718281828\ldots$
\lim_{x \to 0^+} \frac{|x|}{x}	$1$
\lim_{x \to 0^-} \frac{|x|}{x}	$-1$

When the two sides disagree, the two-sided limit is an error; ask for one side with 0^+ or 0^-.

Sums and binomials

Input	Result
\sum_{k=1}^{100} k^2	$338350$
\sum_{k=0}^{10} \binom{10}{k}	$1024$
5!	$120$

Sums are exact and allow up to 1,000,000 terms. The body of a sum is one term: write \sum_{k=1}^{3} (k + 1) for $\sum (k+1)$.

Determinants

\det\begin{pmatrix}1&2\\3&4\end{pmatrix}

$$-2$$

\begin{vmatrix}…\end{vmatrix} is the same. Exact, up to 8×8.

See also

• Syntax
• Known limits: no higher or partial derivatives, no indefinite integrals in the calculator