Calculus Basics Jeopardy

Memorizing Trig Identities

100

Quotient Identities: cot(x)=

cos(x)/sin(x)

200

Quotient Identities: tan(x)=

sin(x)/cos(x)

300

d/dx(cot(x))=

-csc²(x)

400

∫-sin(x) =

cos(x) +c

500

d/dx(csc(x))=

-csc(x)cot(x)

Derivative Rules

100

According to the chain rule, if h(x) = f(g(x))

h'(x)=f'(g(x))g'(x)

200

Exponent Rules: f(x)= e^x then f'(x)=

e^x

300

Power Rule: f(x)= xⁿ then f'(x) equals

nx^n-1

400

Product Rule: h(x)=f(x) ⋅ g(x) then h'(x) equals

f'(x) ⋅ g(x) + f(x) ⋅ g'(x)

500

Log rules: If f(x) = log_a(x) then...

f'(x)=1/(ln(a))x

Unit Circle application

100

sec(330)=

(2√3)/3

200

tan(3pi/2)

undefined

300

arcsec(-2)=

120

400

csc(-3pi)

undefined

500

sec(-540)=

-1

Integrals

100

Solve: ₁∫¹ cos(x)+arctan(x)dx =

0 

200

Solve: ∫2cos(3x)dx

2sin(3x)/3 +c

300

Solve: ∫tan(x) dx

ln(|sec(x)|)+C

400

Solve: ∫5x+5 dx

5x(x+2)/2 +c

500

What must every indefinite integral contain in the answer?

+ c