Calculus

Derivatives

100

4x⁵-3x+7

20x⁴-3

200

(x³+4/x)^1/2

(1/2)(3x²-4/x²)^-1/2

300

tan(2x+4)

sec²(2x+4)(2)

400

(5x³-12x⁵)/(x-2)³

((x-2)³(15x²-60x⁴)-(5x³-12x⁵)(3(x-2)²))/(x-2)⁶

500

(2x-3)²sin(4x²)

4(2x-3)sin(4x²)+(2x-3)²(cos(4x²)8x)

Formulas

100

Power Rule

f(x)=cxⁿ

f'(x)=cnx^n-1

200

Distance Formula

((x₂-x₁₎²+(y₂-y₁)²)^1/2

300

Chain Rule: if y=f(g(x))

y'=f'(g(x))g'(x)

400

Product Rule: y=f(x)g(x)

y'=f(x)g'(x)+g(x)f'(x)

500

Quotient Rule: y=f(x)/g(x)

y'=g(x)f'(x)-f(x)g'(x)/(g(x))^2

Limits

100

limit as x approaches 4 of f(x)=(x²-3x-4)/(x-4)

3

200

limit as x approaches 0 of f(x)=13

13

300

limit as x approaches 9 of f(x)=(x)^1/2-3/x²-81

1/18

400

limit as x approaches 3 for f(x)=2x-15

-9

500

the formal definition of a derivative

lim as h approaches 0 of (f(x+h)-f(x))/h

Pre Calc

100

the shape of a quadratic function

parabola

200

The slope of a vertical line

Undefined

300

The quadratic formula ax²+bx+c=0

x=(-b (+/-) (b²-4ac)^1/2)/2a

400

all possible input values for a function

domain

500

Factor 12x^2+29x+14

(4x+7)(3x+2)

Misc.

100

The name of Ms. Thompson's dog.

Aster

200

Ms. Thompson's favorite tv show as a child

American Idol

300

The capital of Kentucky

Frankfort

400

The upcoming superbowl halftime show will be performed by

Rihanna

500

A googol

1 followed by 100 0's, 10¹⁰⁰