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# LateX Derivatives, Limits, Sums, Products and Integrals

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
$$\oiint \oiiint$$