105 cheat sheet 0

bridging

Exponents

$$a^n = \text {a multiplied n times}$$

if a is a negative integer:

$$a ^{-n} = \frac {1} {a^n} = \frac {1} {\text {a multiplied n times}}$$

If a = 0

• if a is negative, answer is -1

$$a^0 =1$$

Properties of Exponents

$$(a^n)^m = a^{nm}$$

$$a^na^m = a^{n+m}$$

$$\frac {a^n}{a^m} = a^{n-m}$$

$$(ab)^n =a^nb^n$$

$$(\frac {a}{b})^n = \frac {a^n}{b^n}$$

$$(\frac {a}{b})^{-n} = (\frac {b}{a})^n = \frac {b^n}{a^n}$$

Logarithm

$$x =b^y \text { equivalent to } y=log_bx$$

Derivatives

Differentiation

• 2x^2 -> 4x

e^ax -(derivative)-> a e^ax

Non decreasing gradient since function is non-negative

Integration

• x-> x^2/2 + c

  • Where c is a constant