
Understanding Derivatives of Vector-Valued Functions

Interactive Video
•
Mathematics
•
9th - 12th Grade
•
Hard

Olivia Brooks
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in finding the derivative of a vector-valued function?
Rewrite the function in terms of 't'
Evaluate the function at t=0
Find the integral of the function
Apply the chain rule
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When applying the power rule to find the derivative, what is the derivative of 5t^(-2)?
10t^(-3)
-10t^(-3)
-5t^(-3)
5t^(-3)
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the derivative of a vector-valued function represent geometrically?
A normal vector
A tangent vector
A parallel vector
A perpendicular vector
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example with X, Y, and Z components, what is the derivative of cosine t?
-cosine t
sine t
-sine t
cosine t
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the value of the tangent vector at t = pi/2 for the given example?
(3, 0, pi)
(-3, 0, -pi)
(3, 0, -pi)
(-3, 0, pi)
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What rule is used to find the derivative of 3 tangent 7t?
Power rule
Chain rule
Quotient rule
Product rule
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of the natural log of t?
1/t
t^2
t
ln(t)
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