Differentiation

Product and Quotient Rule

100

f(x) = e^x ln(x)

f'(x) = e^x 1/x + ln(x) e^x

200

y = sqrt(x) * ln(x)

dy/dx = x^1/2 * 1/x + ln(x) * 1/2 x^-1/2

300

y = cos(x)/e^x

dy/dx = e^x (-sin(x)) - cos(x) e^x/(e^x)²

400

f(x) = (x⁵-3x²)(2x³-x+1)

f'(x) = (x⁵-3x²)(6x² - 1) + (2x³-x+1)(5x⁴ - 6x)

500

f(x) = (3x⁴-x²)/e^2x-4

e^2x-4 * (12x³-2x) - (3x⁴-x²)(2e^2x-4)/(e^2x-4)²

Chain Rule

100

y=e^3x

dy/dx=3e^3x

200

f(x)=sin(x²)

f'(x)=cos(x²)*2x

300

f(x)=(x²+2)³

f'(x)=3(x²+2)² x (2x)

400

y=sin(cos(x))

dy/dx = cos(cos(x)) x (-sin(x))

500

f(x) = cos(e^3x)

f'(x) = -sin(e^3x) x (e^3x) x 3

Implicit and Parametric

100

2y = 3x³

dy/dx = 9x²/2

200

sin(y)=cos(x)

dy/dx = -sin(x)/cos(y)

300

x(t) = ln(t²)

y(t) = e^2t

dy/dx = 2e^2t/(1/t² x 2t)

400

e^3y = sin(x²+1)

dy/dx = cos(x²+1) x 2x / 3e^3y

500

x(t) = cos(t³)

y(t) = sin(t²-2t)

dy/dt = cos(t²-2t) x (2t-2) / -sin(t³) x 3t²

Te Reo

100

What colour is kōwhai?

Yellow

200

If someone asks you “Kei te pēhea koe?” How could you reply?

Answer how you are

300

If someone is whā tekau mā ono years old, how old are they?

46

400

Who wrote the haka “Ka Mate”?

Te Rauparaha

500

What is the Māori name for Wellington?

Te Whanganui-a-Tara

Something Random

100

What natural language has the fewest syllables with only 55?

Te Reo Māori

200

What planet in the solar system has the largest mountain? Bonus points if you can name the mountain.

Mars, Olympus Mons

300

Bluetooth is named after Harold Bluetooth. What did Harold Bluetooth do?

Viking king. United the kingdoms of Norway and Denmark.

400

What country has more lakes than all other countries combined?

Canada

500

What is the most recent country to switch the side of the road they drive on? Bonus points if you can name the year it happened.

Samoa, 2009