CALCULUS JEOPARDY

Chain Rule

100

d/dx(64sin(x⁴))

256x³cos(x⁴)

200

d/dx(x⁴+5x)¹⁰

10(x⁴+5x)⁹(4x³+5)

300

d/dx(sin√(1+cosx))

-(sin(x)cos(√1+cos(x)))/(2√1+cos(x))

400

d/dx(1+x⁵cotx)⁻⁸

(8x⁴(xcsc²x-5cotx))/(x⁵cotx+1)⁹

or

-8(5x⁴cotx-x⁵csc²x)/(x⁵cotx+1)⁹

500

d/dx(cot(14x⁸+9x³))

-(112x⁷+27x²)csc²(14x⁸+9x³)

Product Rule

100

d/dx(16x²)(3x⁵)

336x⁶

200

d/dx((9x+4x²)(34x⁵-3))

(9+8x)(34x⁵-3)+170x⁴(9x+4x²)

OR

952x⁶+1836x⁵-24x-27

300

d/dx(1+x^3/2)(x^-3-2x^1/3)

-(22x^11/2+4x⁴+9x^13/6+18x^2/3)/6x^14/3

400

d/dx(sin(x)+cos(x))(3x³+3)

9x²(sin(x)+cos(x))+(3x³+3)(cos(x)-sin(x))

500

d/dx(cot(x)+sin(x)+4x⁵+14x³)(tan(x)+8x+4x²)

(-csc²(x)+cos(x)+20x⁴+42x²)(tan(x)+8x+4x²)+(sec²(x)+8+8x)(cot(x)+sin(x)+4x⁵+14x³)

Calculus Trivia

100

In what century was calculus invented?

17th century

200

What is the broadest definition of Calculus?

a) The study of operations and applications

b) The study of change

c) The study of shape

d) the study of collections of data

B) The study of change

300

Who are the two people credited with inventing calculus?

Isaac Newton and Gottfried Leibniz.

400

What's the difference between using (y₂-y₁)/(x₂-x₁) and using derivatives?

You can use (y₂-y₁)/(x₂-x₁) when finding the slope of a secant line and a derivative when finding the slope of the tangent line at a specific point.

500

What is needed for a limit to exist? (include three parts)

1. F(x) must exist at that point

2. The limit from the left and the right must exist and be the same

3. F(x) must equal the limit at that point

Product and Chain Rule

100

d/dx(3(6xe^x)²

216x(x+1)e^2x

200

d/dx((x²+1)⁷(9x⁴))

126x⁵(x²+1)⁶+36x³(x²+1)⁷

or

18x³(x²+1⁶)(9x²+2)

300

d/dx((1+4x)³(12x²-1))

12(1+4x)²(12x²-1)+24x(1+4x)³

400

d/dx((x²+1)⁷(9x⁴))

18x³(x²+1)⁶(9x²+2)

or

36x³(x²+1)⁷+126x⁵(x²+1)⁶

500

d/dx(sin(x)+4x²)(cos(x)+3)⁵

(cos(x)+8x)(cos(x)+3)⁵-5sin(x)(cos(x)+3)⁴(sin(x)+4x²)