Derivative Rule Jeopardy

Trig rules

100

Sin u

Cos u · u'

200

dy/dx   4sin(4x) 

16 cos (4x)

300

Tan u

Sec² u · u'

400

csc u

-csc u · cot u · u'

500

arc-sinu

(u')/sqrt(1-u^2)

More trig rules

100

Cos u

-sin u · u'

200

sec u

(sec u) · (tan u) · u'

300

cot u

-csc² ⋅ u'

400

dy/dx (sinu/cosu)

sec²u ⋅ u'

500

arc-tan

(u')/(1+u^2)

Constant rules

100

Cu

C

200

C

0

300

X 

1

400

a^u

(lna) ⋅ a^u ⋅u'

500

dy/dx 10^(3x^2)

(ln10) ⋅ 10^(3x^2) ⋅ 6x

Algebraic Rules

100

xⁿ

nx^(n-1)

200

dy/dx (u ⋅ V)

(u' ⋅ v) + (V' ⋅ u) 

300

dy/dx f(u(x))

f'(u(x')) 

400

Quotient rule (using "V" and u)

((V⋅u')-(u⋅V'))/V^2

500

dy/dx (x^2 ⋅ x^3)

5x⁴

Misc

100

e^u

e^u ⋅ u'

200

e^x (simplest form)

e^x

300

ln(u)

(u')/u

400

log_au

(u')/(lna⋅u)

500

dy/dx ln( (x-2)^2/((x^2 +1)^(1/2)))

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