Holiday 1

For this first Holiday blog I'm going to review derivatives

Derivatives are taken by using certain rules
The Power rule:

what you do for the power rule is multiply x by the exponent and subtract 1 from the exponent

ex: y = x^2
y'= 2x

f(x) = 6x^7
f'(x)= 42x^6

The Product rule:
first (f'(second)) + second (f'(first))
An equation using the product rule would look like this:
y=(6x^2 + 2)(9x)
6x^2 + 2 (9) + 9x (12x)
54x^2 + 18 + 108x^2
162x^2 + 18

The Quotient rule:
bottom(f'(top) - [top(f'(bottom)]/bottom^2
Ex: 3x^3/x^2
x^2(9x^2)-[3x^3(2x)]/x^4
9x^4 - 6x^4/x^4
3x^4 / x^4 = 3

The Chain rule:
A function raised to an exponent: (6x^2 + 4x)^2
multiply exponent to outside, recopy inside, multiply by derivative of the inside
2(6x^2 + 4x) (12x + 4)

That should basically cover what we have learned concerning derivatives