Intro to Calculus

Derivative Rules

100

Which derivative rule would you use to solve f(x) = 5x^3?

Power rule, constant multiple rule

200

Which derivative rule would we use to solve y=4?

Constant rule

300

Which derivative rule would you NOT use to solve f(x) = x + 3x^2?

Sum rule, power rule, constant multiple rule

400

Which derivative would be used to solve the following: f(x)=sin(3x²)

Chain rule, constant multiple rule, power rule, sin rule

Intergral

100

∫x2dx

x³/3 + C

200

∫√x dx

2x^3/2/3 + C

300

∫1/x⁹dx

-1/(8x8) + C

400

∫tanxsecxdx

secx + C

Derivative

100

Find the derivative f(x) = x³-3x²

f'(x) = 3x² - 6x

200

f(x) = (x-3)/(x²+1)

f'(x) = (-x² + 6x + 1)/(x² + 1)²

300

If y = 2x-x²tanx what is y'? 

y' = 2 - 2xtan(x) - x2sec2(x)

400

Find the derivative x²(x²-1)³

(2x)(x² - 1)²(4x² - 1)

Just for fun

100

What are the first 15 digits of pi 

3.14159265358979

200

What are the four concepts of calculus? (Name 2) 

limits, functions, derivatives, integrals, and infinite series.

300

Who are the two mathematicians credited with the discovery of calculus?

Isaac Newton and Gottfried Leibniz

400

What is the only number that has the same number of letters as it’s meaning?

Four