Calculus

Basic Derivatives

100

What is the derivative of y = 3x² ?

y' = 6x

200

Find the derivative of f(x) = 5

0

300

Find the derivative of f(x) = 6x³ + x - 2

18x² + 1

400

Find the derivative of f(x) = -x³+4x²-6x+5

-3x²+8x-6

500

Find the derivative of f(t)=4t^-1-(1/6t^-3)+8t^-5

f(t')= -4t^-2+(1/2t^-4)-40t^-6

Product and Quotient Rule

100

Find the derivative of f(x)=x+1/sq root(x)

x-1/2x sq root(x)

200

f(x) = (3x - 2x²)(5 + 4x)

-24x² + 4x + 15

300

Find the derivative of y = (5x - 2)/(x² + 1)

(-5x² + 4x + 5)/(x² + 1)²

400

Find the derivative of f(x) = (2x + 5)/(x)^1/2

(2x - 5)/(2x^3/2)

500

Find the derivative using the product rule of (4-2x^-5)(-2x⁵)

-40x⁴

Chain Rule

100

Find y' if y = (3x - 9)⁴

12(3x - 9)³

200

Find the derivative of f(x)=(3x2–4x+5)8

8(3x2–4x+5)7⋅(6x−4)

300

Find y' if y = (9x² + 4)^1/3

(6x)/(9x² + 4)^2/3

400

f(x) = (3x⁴-4)⁴(5x⁵+2)

x³(3x⁴-4)³(315x⁵-100x+96)

500

Use chain rule to find thr derivative at x=3 of (x)/(1-x)²

3/4

Maximum and Minimums

100

Find the max y=x³-2x²+2

(0,2)

200

Find the absolute max of -9x/x²+9 on the interval of [0,2]

(0,0)

300

Find the relative min of (x+2)^2/3

(-2,0)

400

Find the relative min of x²/2+4x+4

(-4,-4)

500

Find the absolute min(s) and max(s) of y=x³+9x²+24x+14 on the interval of [-5,-2]

mins (-5,-6) (-2,-6)

max (-4,-2)

Fun Facts

100

How tall is Garrett?

6'6''

200

What was the name of Jack's dog?

a. Fenway

b. Hot Dog

c. Buster

d. clifford

Fenway and Buster

300

What size waist is Roche?

a. 50

b.40

c. 32

d.36

32

400

How many licks does it take to take to get to the center of a tootsie pop?

364

500

What did Jack get struck by while riding his bike down the street?

a.Bird

b.Golf Ball

c.Car

d. Man in a wheelchair

c.Car