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Chain Rule
Product/Quotient Rule
Implicit Differentiation
Misc Stuffy Stuff
Word Problems
100
Find Derivative of sin(x^2)
cos(x^2)*2x
100
find f'(x) when f(x)=(x+2)*x^2 Simplify Fully
3x^2+4x
100
How do we write the derivative of x with respect to y?
dx/dy
100
What is the conceptual idea behind linearization?
Use a tangent line to find the values on a graph that are hard to calculate by hand.
100
The population of people in the USA follows an exponential function. If in the year 2000 the population is 300 million and 350 million in the year 2010 what is the K value?
Either ln(7/6)/10 OR 0.015
200
Find Derivative of (3x+1)^5
15(3x+1)^4
200
f(x)=(x^3+2)(x^7-7x^4) DO NOT SIMPLIFY!
3x^2*(x^7-7x^4)+(x^3+2)*(7x^6-28x^3)
200
If we were given the following equation: s^2+t=t^3 and we wanted to find ds/dt, how do we find the derivative of s^2?
2s*ds/dt
200
Find the derivative of ln(e^arctan(x))
1/(1+x^2)
200
The volume of a cup is falling at a rate of x feet per second. At what rate is the radius changing? What would the change in volume per second be symbolically? What are the units
dV/dt ft^3/s
300
Find f'(x) f(x)=(x^3-1)^(1/2)
1/2*(x^3-1)^(-1/2)*3x^2
300
f(x)=sin(x)/tan(x) find f'(x) Simplify your answer fully!
-sin(x)
300
Find dy/dx y^4-3y^3-x=3
dy/dx=1/(4*y^3-9y^2)
300
Use linearization to estimate the square root of 17.
33/8 or 4.125
300
There are 7000 Borg cubes in the immediate vicinity of Captain Picard's enterprise. 5 weeks later there are only 5000 Borg cubes remaining. Create an exponential model to tell the following: How many Borg cubes can we expect after 10 weeks? About how long will it take Picard to destroy all the cubes?
About 3571 Borg Cubes after 10 weeks About 142 or more weeks to destroy all
400
find f'(x) if f(x)=1/(sin(cos(4x-2))
(sin(cos(4x-2))^-2*cos(cos(4x-2))*sin(4x-2)*4
400
True or False? The quotient rule can be remembered as hiDlo-LoDHi/Lo^2
False
400
Find the equation of the tangent line at (0,Pi/2) cos(y)=x
y=-x+Pi/2
400
Use a differential to estimate how the Area of a circle changes when it's radius changes from 3 to 3.1.
0.6*Pi
400
Rachel decides to quit teaching and instead to become a beekeeper and start selling barrels of honey. The barrels are filled by the bees at a rate of 100 cm^3/hr. If the barrel Rachel uses has a radius of 50 cm, what is the rate the height is changing when it is 100 cm full? V=pi*r^2*h
1/25*Pi cm/hr
500
Find f'(x) when f(x)=(tan(sec(x^3)))^(1/2)
3/2*(tan(sec(x^3))^(-1/2)*sec^2(sec(x^3))*sec(x^3)*tan(x^3)*x^2
500
find the derivative of (cos(x^2))/(sin(x)
(-2x*sin(x^2)*sin(x)-cos(x^2)*cos(x))/sin(x)^2
500
Find the equation of the NORMAL line at (5/3,3) for 2xy-y^2=1 Use point slope form
y-3=-4/9*(x-5/3)
500
Find the limit as x approaches 0 of 5*tan(4x)*cos(4x) / (8x*cos(x)) You must show all work!
5/2
500
Rachel and her roommates are hanging up Christmas lights. She's standing on top of a ladder that is 15 feet long and pressed up against the side of her house. The bottom of the ladder where she has all of her supplies is 10 feet away from the house. Unfortunately, Rachel has an argument with her roommate and he kicks the ladder towards the house making it move towards the house at a rate of 1/4 ft per second. Rachel screams for dear life as she and the top of the ladder start moving up the wall. At this point, how fast are the ladder and Rachel moving up the wall?
7/4*(176)^-1/2=0.13