True/False: The Chain Rules, implicit differentiation, and all derivative rules can be combined in one single problem.
What is True
100
What is the interpretation of d^2y/dx^2?
What is Second Derivative
200
Explain the best way to prove that the derivative of cos(x) is -sin(x).
What is By using Limits
200
d/dx[sin^2(x)]
What is 2sin(x)cos(x)
200
What is the implication of a second derivative in terms of physics?
What is acceleration
200
s(t) always stands for what?
What is position
300
d/dx[sin(cos(tan(x))]
What is -cos(cos(tan(x))sin(tan)sec^2(x)
300
What units are required for acceleration?
What is ft^2/s
300
Explain what a related rate is?
What is A word problem where certain rates and variables are in a relation with each other with a common formula in place with certain given dimensions.
400
What is the tangent of (-pi/2)?
What is undefined
400
Under what mathematical conditions is the chain rule necessary?
What is When two or more functions are composed together.
400
Explain how you can tell if a particle is slowing down in terms of velocity and acceleration.
What is opposite signs.
400
True/False: You must always use the Chain Rule with related rate problems.
What is True
500
d/dx[sec(x)] = ?
What is sec(x)tan(x)
500
True/False: The Chain Rule and all other derivative rules cannot be combined together.
What is False
500
Explain what conditions would require implicit differentiation.
What is When you are taking the derivative in terms of x and y.
500
Explain why you cannot substitute the given numerical data into a related rate problem.
What is Because of the rates. We must take the derivative first so that the chain rule can be applied this taking into account the given and existing rates.