The Chain Rule
Implicit Differentiation
Higher Derivatives
Related Rates
AP Calculus Review
100
Differentiate: y = sin(x^2)
What is 2xcos(x^2)
100
Would the following require implicit differentiation? Differentiate: x + y = 0
What is yes
100
Identify the meaning of the following: S(t) = ? v(t) = ? a(t) = ? j(t) = ?
What is position, velocity, acceleration, and jerk
100
What do you do if you have 2 unknown variables within a formula that you are trying to take the derivative of?
What is use geometry to eliminate one of the variables
100
What are the three types of discontinuity?
What is jump, infinite, and removable
200
Differentiate y = sin^2(x)
What is 2sin(x)cos(x)
200
What is the capitol of Kentucky?
What is Frankfurt
200
In general, what is another way to describe the following: "A rate of change of a rate of change"
What is a second derivative
200
What unit should angles be converted to in a related rate problem?
What is radians
200
Name 4 types of functions that are continuous at every number in their domains
What is polynomial, rational, root, and trigonometric
300
How many times would the chain rule be necessary here? sin(cos(tan(x))
What is 3
300
Differentiate: y = sin(x + y). Leave y' alone.
What is cos(x + y)(1 + y')
300
What is the 8th derivative of cos(x)?
What is cos(x)
300
With given values for x and y, when should you typically plug these values in?
What is after you take the derivative of the function
300
What is the derivative if tan(x)?
What is sec^2(x)
400
True/False: The Power Rule can be combined with the Chain Rule?
What is True
400
Under what type of situation would you use implicit differentiation on both x and y?
What is on related rate problems
400
How would you express the nth derivative in terms of notation?
What is f^n (x)
400
At what temperature does the Celsius scale equal the Farenheight scale?
What is -40
400
What is the largest state east of the Mississippi?
What is Georgia
500
In general, what type of situation requires the use of the chain rule?
What is when you have a composition of two or more functions
500
If I were to ask you to solve for x', how would you express this in terms of Leibniz Notation?
What is dx/dy
500
How do you tell if a particle is speeding up?
What is the velocity and the acceleration will have the same sign
500
What geometrical principle is usually used in related rate problems to eliminate a variable?
What is similarity
500
The slope of the tangent line finds what kind of velocity?
What is instantaneous
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