# Math-Linux.com

Knowledge base dedicated to Linux and applied mathematics.

Home > Latex > FAQ > Latex - FAQ > How to write LateX Derivatives, Limits, Sums, Products and Integrals

## How to write LateX Derivatives, Limits, Sums, Products and Integrals

How to write LateX Derivatives, Limits, Sums, Products and Integrals ?

### 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 $\frac{\partial^{k} f}{\partial x^k}$

$$\frac{\partial^{k} f}{\partial x^k}$$

### 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)$

$$\min_{x \in [\alpha,\beta]}f(x)$$

### 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 $$\sum^k_{i=1}\sum^l_{j=1}\,q_i q_j$$

$$\sum^k_{i=1}\sum^l_{j=1}\,q_i q_j$$

### 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 $$\prod^k_{i=1}\prod^l_{j=1}\,q_i q_j$$

$$\prod^k_{i=1}\prod^l_{j=1}\,q_i q_j$$

### Integrals

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 $$\oint$$

$$\oint$$

### Closed surface and volume integrals

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