Derivative Jeopardy

Product Rule

100

d/dx((x+2)²)

2(x+2) or 2x+4

200

d/dx(x³e^3x)

3x²e^3x(x+1)

300

d/dx(sec²(x))

2sec²(x)tan(x)

400

d/dx(sqrt(x)*12x)

18sqrt(x)

500

d/dx(sec(x)*tan(x))

sec(x)tan²(x)+sec³(x)

Quotient Rule

100

d/dx(sin(x)/cos(x))

sec²(x)

200

d/dx(x/x²)

-1/x²

300

d/dx(e^x/(2x+3))

(e^x(2x+3)-e^x(2))/(2x+3)²

400

d/dx((x²+3x+1)/(x³−2x))

−(x⁴+6x³+5x²−2)/(x3−2x)²

500

d/dx((x³+2x)/(x²−4))

(x⁴−14x²−8)/(x2−4)²

Randoms

100

d/dx(e^4x)

4e^4x

200

d/dx(e^pi)

0

300

Using the limit definition of derivative, d/dx(3x-x²) looks like this (just set it up, do not compute)

lim_h->0 [(3(x+h)-(x+h)²)-(3x-x²)]/h

400

If I asked you to determine the speed (in miles per hour) of a car whose position, where t=hours, is defined by

p(t)=t²+3t+2

what would its speed be exactly 5 hours after it started?

13 miles per hour

500

find the equation of the tan line of f(x) = x² at the point (2,4)

y=4x−4

Chain Rule

100

d/dx((x²+2x+1)²¹)

21(2x+2)(x²+2x+1)²⁰

200

d/dx[((x)/(x+1))⁵]

5x⁴/(x+1)⁶

300

d/dx(e^{(x^3+3)})

3x²e^{(x^3+3)}

400

d/dx(sqrt(x³-2x²+3))

x(3x-4)/2(sqrt(x³-2x²+3))

500

d/dx(tan(sqrt(x²+e^x)))

 -sin(sqrt(x²+e^x)*(2x+e^x)/2sqrt(x²+e^x)

Trig stuff

100

d/dx(2cos(x)+3sin(x))

-2sin(x)+3cos(x)

200

d/dx(tan(2x))

2sec^2(x)

300

d/dx (cot(x))

-csc^2(x)

400

d/dx(-e^x(sin(x))

-e^xcos(x)-e^xsin(x)

500

Find the equation of the tangent ine to g(x)=cos(3x) at the point (pi/6,0)

y=-3x+pi/2