Derivative Jeopardy

Product/Quotient

100

f(x) = (2x³+3)(3x²)

What is f'(x)?

f'(x) = 30x⁴ + 18x

200

f(x) = (x³+5)(x²+2)

What is f'(x)? 

f'(x) = 5x⁴+6x²+10x

300

f(x)=10/(3x-2)

What is f'(x)?

f'(x) = -30/(3x-2)²

400

f(x) = (x²)/(3x³+2)

What is f'(x)?

f'(x) = (-3x⁴+4x)/(3x+2)²

500

f(x) = (4x²+x³)/(3x³-4)

What is f'(x)?

f'(x) = (-12x⁴-12x²-32x)/(3x³-4)²

Chain

100

y = (x²+3)³

What is y'?

y' = 6x(x²+3)²

200

y = (-3x³+2)⁵

What is y'?

y' = -45x²(-3x³+2)⁴

300

y = (2x+2)^1/2

What is y'?

y' = 1/(2x+2)^1/2

400

y = (-3x+5)^-4

What is y'?

y' = 24x/(-3x²+5)⁵

500

y = ³√(-6x³+4)

What is y'?

y' = - (6x²)/(-6x³+4)^2/3

Addition/Subtraction/Power

100

f(x) = x²+1

What is f'(x)?

f'(x) = 2x

200

f(x) = 3x⁴+x²+2

What is f'(x)?

f'(x) = 12x³+2x

300

f(x) = 12x⁴-5x³+x-100

What is f'(x)?

f'(x) = 48x³-15x²+1

400

f'(x) = (-5/3)x^3/2+(2/7)x

What is f'(x)?

f'(x) = -3x^1/2 + (2/7)

500

f(x) = (4/5)x+4x^-2+6x^-3

What is f'(x)?

f'(x) = (4/5)-(8/x³)-(18/x⁴)

Trig/Inverse Trig

100

y = 4 sin (x) - 7 cos (x)

What is y'?

y' = 4 cos (x) + 7 sin (x)

200

y = cos 2x⁵

What is y'?

y' = -sin (2x⁵)(10x⁴)

300

y = csc 4x⁸

What is y'?

y' = -csc (4x⁸) cot (4x⁸)(32x⁷)

400

y = cot^-1 6x³

What is y'?

y' = (-18x²)/(1+36x⁶)

500

y = sin^-1 (4x⁵)

What is y'?

y' = (1)/(²√1-16x¹⁰)

Exponential/Logarithmic

100

f(x) = e^{x^4}

What is f'(x)?

f'(x) = (e^{x^4})(4x³)

200

f(x) = 5^{3x^6}

What is f'(x)?

f'(x) = 5^{3x^6} ln (5) 18x⁵

300

f(x) = ln 2x⁴

What is f'(x)? 

f'(x) = 4/x

400

f(x) = log₂ x⁶

What is f'(x)? 

f'(x) = 6/(x ln (2))

500

f(x) = log₆ 7x⁴

What is f'(x)?

f'(x) = 4/(x ln(6))