Honors Calculus Jeopardy

Derivatives

100

What is the derivative of 6x⁴ 

24x³

200

What is the derivative of (x³+2)^1/2

1/2(x³+2)^1/2(3x²)

300

What is the derivative of (x+1)/(x-1)?

((x+1)(x)-(x-1)(x))/(x-1)²

400

What is the second derivative of 6x⁸+9x

336x

500

What is the second derivative of (3x⁴/4x²)?

((4x²)(8x(36x)-12x(8))-(4x²(12x³-3x⁴8x)(8x²8x))/(((4x²)²)²)

Intergrals

100

what is the integral of 2x?

x²+C

200

what is the integral of (2)/(4x)dx

(1/2)ln(x)+C

300

what is the integral of (3x²/2)+(4/x)dx?

(3x²/2)+4ln(x)+C

400

what is the integral of e^xdx

e^x+C

500

what is the integral of the square root of x?

(2x√ x)/(3)+C

Trig Derivatives

100

what is the derivative of sinx dx?

cosx

200

what is the derivative of cscx?

-cscxcotx

300

what is the derivative of sin(3x)+cos2x

3cos(3x)−2sin(2x)

400

find the derivative of (tanx)/(cotx)?

2sec²x tanx

500

find the derivative of 6x²+sin3xtan4x

4sec2(4x)sin(3x)+3cos(3x)tan(4x)+12x

Trig Integrals

100

what is the integral of sinx

-cosx+C

200

what is the integral of cosx+3x

sinx+(3x²/2)+C

300

what is the integral of secxtanx+e^x

(1/cosx)+e^x+C

400

what is the integral of cosx+(1/3x)?

sinx+ln(1/3x)+C

500

what is the integral of (sinx)/(tanx)

sinx+C