Calc Review 2/3

Log Derivatives

100

ln(x)

1/x

200

log_3(x)

1/(xln(3)

300

log_5(x^2)

2/(xln(5))

400

ln(x^3)

3/x

500

x^3log_5(x)

3x^2log_5(x)+x^2/ln(5)

Exponential Derivatives

100

e^x

e^x

200

e^(3x)

3e^(3x)

300

4^x

4^xln(4)

400

e^(x^2)

2xe^(x^2)

500

5^(x^2+3x)

5^(x^2+3x)(2x+3)(ln5)

Trig Derivatives

100

sin x

cos x

200

cos x

-sin x

300

sin x cos x

cos^2(x)-sin^2(x)

400

sec x

sec x tan x

500

cot x

-csc^2(x)

Implicit Derivatives

100

2x=3y

2/3

200

5x^2+y=8

dy/dx=-10x

300

x^2+y^2=3

dy/dx=-x/y

400

An circular ice sheet is melting. The radius is decreasing at a rate of 5 meters per hour. When the radius is 20 meters, how fast is the area shrinking?

-200pi

500

x^3y^2=2y

dy/dx=(3x^2y^2)/(2-2x^3y)

Grab Bag

100

These 2 teams are playing in the super bowl

Eagles and Chiefs

200

Write pi to 5 decimal places

3.14159

300

The chemical symbol for Potassium

K

400

She was the first woman to win a Nobel Prize

Marie Curie

500

It is illegal for a single woman to do this on Sundays in Florida

Skydive