Derivatives
4x5-3x+7
20x4-3
Power Rule
f(x)=cxn
f'(x)=cnxn-1
limit as x approaches 4 of f(x)=(x2-3x-4)/(x-4)
3
the shape of a quadratic function
The name of Ms. Thompson's dog.
Aster
(x3+4/x)1/2
(1/2)(3x2-4/x2)-1/2
Distance Formula
((x2-x1)2+(y2-y1)2)1/2
limit as x approaches 0 of f(x)=13
13
The slope of a vertical line
Undefined
Ms. Thompson's favorite tv show as a child
American Idol
tan(2x+4)
sec2(2x+4)(2)
Chain Rule: if y=f(g(x))
y'=f'(g(x))g'(x)
limit as x approaches 9 of f(x)=(x)1/2-3/x2-81
1/18
The quadratic formula ax2+bx+c=0
x=(-b (+/-) (b2-4ac)1/2)/2a
The capital of Kentucky
Frankfort
(5x3-12x5)/(x-2)3
((x-2)3(15x2-60x4)-(5x3-12x5)(3(x-2)2))/(x-2)6
Product Rule: y=f(x)g(x)
y'=f(x)g'(x)+g(x)f'(x)
limit as x approaches 3 for f(x)=2x-15
-9
all possible input values for a function
domain
The upcoming superbowl halftime show will be performed by
Rihanna
(2x-3)2sin(4x2)
4(2x-3)sin(4x2)+(2x-3)2(cos(4x2)8x)
Quotient Rule: y=f(x)/g(x)
y'=g(x)f'(x)-f(x)g'(x)/(g(x))^2
the formal definition of a derivative
lim as h approaches 0 of (f(x+h)-f(x))/h
Factor 12x^2+29x+14
(4x+7)(3x+2)
A googol
1 followed by 100 0's, 10100