Calculus Trivia

Derivatives of Trig Functions

100

d/dx[sinx]

cosx

200

d/dx[tanx]

sec^2x

300

d/dx[cscx]

-cscxcotx

400

d/dx[secx]

secxtanx

500

d/dx[cotx]

-csc^2x

Rules

100

d/dx[f(x)+g(x)] = f’(x)+g’(x)

Sum and Difference Rules

200

Derivative of a Natural Exponential Function 

d/dx[e^x]=e^x

300

d/dx[c]=0, the derivative of y=c is day/dx=0

Constant Rule

400

d/dx[ax^n]=anx^n-1

General Power Rule

500

Recite Quotient Rule, without say low D…

= g(x)f’(x)-f(x)g’(x)/[g(x)]^2

Integrals of Trig Functions

100

Ssin(u) du

-cos(u)+C

200

Stan(u)du

-ln|cos(u)|+C

300

Ssec(u) du

ln|sec(u)+tan(u)|+C

400

Scos(u) du

sin(u)+c

500

Scsc(u) du

-ln|csc(u)+cot(u)|+C

Theorems

100

What is: a point (c) MUST exists on a continuous graph [A, B]

Intermediate Value Theorem

200

What is added at the end of integrals?

+C

300

Log Rule for Integration

S1/x dx = 

ln|x|+C

400

lim f(x)/g(x) as x approaches c 

= lim f’(x)/g’(x) as x approaches c 

L’Hopital‘s Rule

500

The rate of change in the temp of an object is proportional to the difference between the objects them and the temp of its surroundings. 

Newton’s Law of Cooling

Fun Facts

100

Who founded Calculus?

Isaac Newton

200

What is slope at a tangent line?

Derivative 

300

Does continuity imply differentiability 

false, reversed

400

Calculus is taught by how many teachers in this building?

1

500

What is Mrs. McCall’s favorite lesson?

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