AP Calculus AB Final Project: Chapter 2 Jeopardy

Simple Derivatives

100

Find the derivative of: 

f(x) = 10x(5x²)

What is f'(x) = 150x²?

200

Find the derivative of: 

f(x) = -5x³ - 2x²¹

What is f'(x) = -15x² - 42x²⁰?

300

Find the derivative of: 

f(x) = 30x + (4x³ + 3) / 4

What is f'(x) = 30 + 3x²?

400

Find the derivative of: 

f(x) = tan(x)sin(x)cos(x)

What is f'(x) = sin(2x)?

500

Find the derivative of: 

f(x) = 30x / (sin(x)cos(x))

What is f'(x) = (15sin(2x) - 30xcos(2x)) / (cos(x)sin(x))²?

Higher-Order Derivatives

100

Find the third derivative of: f(t) = 3t⁷ − 6t⁴ + 8t³ − 12t

What is f'''(t) = 630t⁴ - 144t + 48?

200

Find d²y/dx² of: 

2x³ + y² = 1 − 4y

What is d²y/dx² = [-6x(y+2)² - 9x⁴] / [y+2]³

300

Find the second derivative of: 

f(x) = cos²(7x)

What is f''(x) = -98cos(14x)?

400

Find the second derivative of: 

f(x) = sin(2x³ − 9x)

What is f''(x) = -sin(2x³ - 9x)(6x² - 9)² + 12xcos(2x³ - 9x)? 

500

Find the third derivative of: 

f(t) = sec(5t)

What is f'''(t) = 625sec³(5x)tan(5x) + 125tan³(5x)sec(5x)?

Tangent Lines

100

Find the tangent line of:

f(x) = cos(2x),

at x = 0

What is y = 1?

200

Find the tangent line of:

f(x) = 3x³ + 7x² + x⁴,

at x = 3

What is y - 225 = 231(x - 3)?

300

Find the tangent line of:

f(x) = 7x / (x² + 12),

at x = 4

 What is y = -x/28 + 8/7?

400

Find the tangent line of:

f(x) = 15x²(30x³ + 15x),

at x = 2

What is y - 16200 = 38700(x - 2)?

500

Find the tangent line of:

f(x) = 2x + sin(2x),

at x = 0

What is y = 4x?

Difficult Chain Rule

100

Differentiate using chain rule:

f(x) = cos(sin(tan(5x²)))

What is f'(x) = -10xsin(sin(tan(5x²)))cos(tan(5x²))sec²(5x²)?

200

Differentiate using chain rule:

y = x(4x+x⁵)^1/3

What is y' = [8x⁵ + 16x] / [3(4x + x⁵)^2/3]

300

Differentiate using chain rule:

f(t) = sin^-4/3(2t / (t² + 10))

What is f'(t) = [8cos(2t / (t² + 10))(t² - 10)] / [3sin^7/3(2t / (t² + 10))(t² + 10)²]?

400

Differentiate using chain rule:

y = sec^-4(4+x³) / 5

What is y' = (-12x²/5)cos⁴(4+x³)tan(4+x³)?

500

Differentiate using chain rule:

y = 10(1+(2-(6+7x⁴)⁹)³)⁵

What is 

y' = -37800x³(1+(2-(6+7x⁴)⁹)³)⁴(2-(6+7x⁴)⁹)²(6+7x⁴)⁸?