Intro to Derivatives Unit Jeopardy

Derivatives

100

2x³

6x²

200

33x⁴

132x³

300

12x²-8x⁴+6x²

36x+32x³

400

2/x

-2x^-2

500

11/x³

-33x^-4

Chain Rule

100

(x+3)²

2x+6

200

sin(x+7)³

3cos(x+7)²

300

e^-2x

-2e^-2x

400

3x(cos(x))

3sin²(x)-3cos²(x)

500

2xe^arctan(x)

2(e^arctan(x)+(e^arctan(x)x/x²+1))

Trig Based

100

tan(x)

sec²(x)

200

3cos(x)

-3sin(x)

300

arcsin²(x)

2arcsin(x)/(sqrt(1-x²)

400

12x(cot(x))

12(cot(x)-xcsc²(x))

500

sqrt(sin(x))

cos(x)/2sin(x)

Logs/Exponential

100

e^x

e^x

200

3ln(x)

3/x

300

2xln(x)

2ln(x)+2

400

ln(7x)²

2/x

500

e^{cos(x)^2}

-e^{cos(x)^2}sin(2x)

Product/Quotient Rule

100

3x(10x)

60x

200

3x/(x²)

-3x²/x⁴

300

10x(cos(x))

-10cos²(x)+10sin²(x)

400

7x/(tan(x))

(7tan(x)-7xsec²(x))/(tan²(x)

500

e^x(12ln(x))

(12e^x/x))+12ln(x)(e^x)