# Q.E.D.

Latin for "end of proof". Common notation is $\square$.

# Calculus

## Leibniz's notation

-   derivative: $$\frac{\operatorname d y}{\operatorname d x}$$
-   higher order: $$\frac{\operatorname d^n y}{\operatorname  d x^n}$$
-   derivative at point $a$: $$\left.\frac{\operatorname d y}{\operatorname d x}\right|_{x=a} = \frac{\operatorname d y}{\operatorname d x}(a)$$
-   integral: $$\begin{align}
                                                    \int y\,dx &= \int f(x)\,dx = F(x) + C_1 \\
                                             \int \int y\,dx^2 &= \int \left ( \int y\,dx \right ) dx = \int_{X\times X} f(x)\,dx = \int F(x)\,dx = g(x) + C_2 \\
  \underbrace{\int \dots \int}_n y\,\underbrace{dx \dots dx}_n &= \int_{\underbrace{X\times\cdots\times X}_n} f(x)\,dx = \int s(x)\,dx = S(x) + C_n
\end{align}$$

## Lagrange's notation

-   derivative: $$f'(x)$$
-   higher order: $$f''(x), f'''(x), f^{(n)}(x)$$

## Euler's notation

-   derivative: $$\operatorname D f$$
-   higher order: $$\operatorname D^n f$$

## Newton's notation

-   derivative: $$\dot{y}$$
-   higher order: $$\ddot{y}$$

## partial derivative

$$\frac{\partial f}{\partial x}, \operatorname D_{xy}f,
\partial_x f, f_{xy}$$


```python

```

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