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High number formula
Advanced mathematics covers many branches of mathematics, so there are many formulas. The following are some commonly used formulas of advanced mathematics:

Calculus section:

1. derivative formula: $ f' (x) = \ lim _ {\ delta x \ to0} \ frac {f (x+\ delta x)-f (x)} {\ delta x} $;

2. Common derivative formulas: $ (x m)' = MX {m- 1} $,$(\sin x)'=\cos x$, $(\cos x)'=-\sin x$, $ (e x)' = e

3. Basic integral formula: $ \ int x m \ Mathrm {d} x = \ frac {m+1} {m+1}+c $,$ \ int \ frac {1} {sin x \.

Linear algebra part:

1. vector dot product formula: $ \ vec {a} \ cdot \ vec {b} = a _1b _1+a _ 2b _ 2+a _ 3b _ 3 $;

2. Matrix multiplication formula: if $A_{m \times n}$ and $B_{n \times p}$, then $ c _ {m \ timesp} = a _ {m \ timesn} \ cdotb _ {n \ timesp} $ where $ c _

3. Determinant formula: If $A$ is a square matrix of order $n$, then $ | a | = \ sum _ {i =1} n (-1) {i+j} a _ {ij} m _ {ij} $,