Derivative Jeopardy

Basic Derivatives

100

y = 3

y' = 0

200

f(x) = 5x² - 2x + 1,000,000

f'(x) = 10x - 2

300

f(x) = 5sin(x) - 4cos(x)

f'(x) = 5cos(x) + 4sin(x)

400

y = 2 ln(x) + 3e^x

y' = 2/x + 3e^x

500

y = 2tan(x) - 5sec(x)

y' = 2sec²(x) - 5sec(x)tan(x)

Product/Quotient Rules

100

f(x) = e^xsin(x)

f'(x) = e^xsin(x) + e^xcos(x)

200

y = e^x / x

y' = (xe^x - e^x) / x²

300

y = 7x²ln(x)

y' = 14xln(x) + 7x²(1/x)

    = 14xln(x) + 7x

400

y = (5x - 2)/(x² + 1)

y' = (-5x²+4x +5)/(x² + 1)²

500

f(x) = x³sin(x)cos(x)

y' = 3x²sin(x)cos(x) + x³cos²(x) - x³sin²(x)

Chain Rule

100

y = (5x - 9)⁴

y' = 20(5x - 9)³

200

y = cos(8x)

y' = -8sin(8x)

300

f(x) = 10e^-2x

f'(x) = -20e^-2x

400

f(x) = 4 ln(x² + 9)

f'(x) = 8x / (x² + 9)

500

y = sin⁸(2x³)

y' = 48x² sin⁷(2x³) cos(2x³)

There's a Trick

100

f(x) = (2 - x³) / x²

f'(x) = -4x^-3 - 1

Write f as 2x^-2 - x

200

y = ln(e^x)

y' = 1

Simplify y = ln(e^x) = x

300

y = sin(x)[csc(x) + sec(x)]

y' = sec²(x)

Distribute: y = 1 + tan(x)

400

f(x) = (x² - 1) / (x - 1)

f'(x) = 1

Simplify f(x)=(x-1)(x+1)/(x-1) = x + 1

500

y = sin²(3x) + cos²(3x)

y' = 0

y = 1 (Pythagorean Identity)

Mixed Bag

100

f(x) = -3x + cot(x)

f'(x) = -3 - csc²(x)

200

f(x) = tan^-1(x)

f'(x) = 1/(x² + 1)

300

f(x) = csc(5x - 1)

f'(x) = -5csc(5x - 1)cot(5x - 1)

400

x³ + y³ = 1

dy/dx = - x²/y²

500

f(x) = sin^-1(x²)

f'(x) = 2x / (1 - x⁴)^1/2