holiday blog 1

hmm... derivatives. yeahhh lets do some of those:

the quotient rule: bottom(f'(top) - [top(f'(bottom)]/bottom^2

2x^4/x^5 =

x^5(8x^3) - [2x^4(4x^3)]/(x^5)^2
8x^8 - 8x^7/x^10
8x/x^10
= 8/x^9

the product rule: first (f'(second)) + second (f'(first))

(3x^2 + 3)(4x) =

3x^2 + 2(4) + 9x(6x)
12x^2 + 8 + 54x^2
= 66x^2 +8

the power rule:

y = 3x^2
y'= 6x

y = 4x^5
y' = 20x^4