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LateX Derivatives, Limits, Sums, Products and Integrals

Sunday 2 April 2023, by Nadir Soualem

derivative iint int integral Latex lim oint prod sum

All the versions of this article: <English> <français>

How to write derivatives in LateX?
How to write sums in LateX?
How to write products in LateX?
How to write integrals in LateX?

Latex derivative

How to write LateX Derivatives ?

Definition	Latex code	Result
First order derivative	$f'(x)$	$f’(x)$
Second order derivative	$f''(x)$	$f’’(x)$
K-th order derivative	$f^{(k)}(x)$	$f^{(k)}(x)$
Partial firt order derivative	$\frac{\partial f}{\partial x}$	$$\frac{\partial f}{\partial x}$$
Partial Second order derivative	$\frac{\partial^2 f}{\partial x^2}$	$$\frac{\partial^2 f}{\partial x^2}$$
Partial k-th order derivative	$\frac{\partial^{k} f}{\partial x^k}$	$$\frac{\partial^{k} f}{\partial x^k}$$

Latex limit

How to write LateX Limits?

Definition	Latex code	Result
Limit at plus infinity	$\lim_{x \to +\infty} f(x)$	$$\lim_{x \to +\infty} f(x)$$
Limit at minus infinity	$\lim_{x \to -\infty} f(x)$	$$\lim_{x \to -\infty} f(x)$$
Limit at $\alpha$	$\lim_{x \to \alpha} f(x)$	$$\lim_{x \to \alpha} f(x)$$
Inf	$\inf_{x > s}f(x)$	$$\inf_{x > s}f(x)$$
Sup	$\sup_{x \in \mathbb{R}}f(x)$	$$\sup_{x \in \mathbb{R}}f(x)$$
Max	$\max_{x \in \[a,b\]}f(x)$	$$\max_{x \in \[a,b\]}f(x)$$
Min	$\min_{x \in \[\alpha,\beta\]}f(x)$	$$\min_{x \in \[\alpha,\beta\]}f(x)$$

Latex sum

How to write LateX sums?

Definition	Latex code	Result
Sum	$\sum$	$$\sum$$
With \limits	$\sum\limits_{j=1}^k A_{\alpha_j}$	$\sum\limits_{j=1}^k A_{\alpha_j}$
Without\limits	$\sum_{j=1}^k A_{\alpha_j}$	$\sum_{j=1}^k A_{\alpha_j}$
Sum from 1 to n	`$$\sum_{i=1}^n$$`	$$\sum_{i=1}^n$$
Sum off n first integers	`$$\sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6}$$`	$$\sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6}$$
Double sum	`$$\sum^k_{i=1}\sum^l_{j=1}\,q_i q_j$$`	$$\sum^k_{i=1}\sum^l_{j=1}\,q_i q_j$$

Latex product

How to write LateX Products ?

Definition	Latex code	Result
Product	$\prod$	$$\prod$$
With \limits	$\prod\limits_{j=1}^k A_{\alpha_j}$	$\prod\limits_{j=1}^k A_{\alpha_j}$
Without \limits	$\prod_{j=1}^k A_{\alpha_j}$	$\prod_{j=1}^k A_{\alpha_j}$
Product from 1 to n	`$$\prod_{i=1}^n$$`	$$\prod_{i=1}^n$$
Product off n first integers	`$$\prod_{i=1}^n i^2{6}$$`	$$\prod_{i=1}^n i^2$$
Double product	`$$\prod^k_{i=1}\prod^l_{j=1}\,q_i q_j$$`	$$\prod^k_{i=1}\prod^l_{j=1}\,q_i q_j$$

Latex Integral

Definition	Latex code	Result
Integral	`$$\int$$`	$$\int$$
Integral limits	$\int_{a}^b f(x)dx$	$$\int_{a}^b f(x)dx$$
Double integral	`$$\iint$$`	$$\iint$$
Double integral with limits	`$$\int_{a}^b\int_{c}^d f(x,y)dxdy$$`	$$\int_{a}^b\int_{c}^d f(x,y)dxdy$$
Double integral with dots	`$$\idotsint$$`	$$\idotsint$$
Triple integral	`$$\iiint$$`	$$\iiint$$
Quadruple integral	`$$\iiiint$$`	$$\iiiint$$
Contour integral	`$$\oint$$`	$$\oint$$

Latex closed surface and volume integrals

To define such integrals, you must use wasysym package
$$\oiint \oiiint$$

Integrale double triple circulaire

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