Derivative Jeopardy

Trig Derivatives

100

sin(x)

cos(x)

200

cos(x)

-sin(x)

300

csc(x)

-csc(x)cot(x)

400

arctan(x)

1/(1+x^2)

500

arccsc(x)

-1/(absolute value(x))(sqrt(x^2-1))

Power Rule

100

x

1

200

4x^5

20x^4

300

3x^7+5x^5+6x^3+2x+1

21x^6+25x^4+18x^2+2

400

(x^2+4x+4)^3

3(x^2+4x+4)^2(2x+4)

500

(tan(x))^2

(2tan(x))(sec(x))^2

Product Rule

100

(x)(1)

1

200

(x)(x)

2x

300

(sin(x))(x)

cos(x)(x)+sin(x)

400

(ln(x))(x^2)

(1/x)(x^2)+(ln(x))(2x)

500

(e^(5x))(tan(x))

(e^(5x))(5)(tan(x))+(e^(5x))(sec(x))^2)

Quotient Rule

100

x/x

0

200

1/x

-x^-2

300

x/(1-x)

((1)(1-x)-(x)(-1))/(1-x)^2

400

(x^2+3)/(x)

((2x)(x)-(x^2+3)(1))/(x^2)

500

(cot(x))/(arcsin(x))

((-sec(x))^2(arcsin(x))-(cot(x))(1/sqrt(1-x^2)))/(arcsin(x))^2

Exponent/Log Derivatives

100

ln(x)

1/x

200

e^x

e^x

300

3e^(4x^3)

3e^(4x^3)(12x^2)

400

log₅(2x^2)

1/((2x^2)(4x)ln(5))

500

e^(sec(x))

e^(sec(x))(sec(x))(tan(x))