# Worksheet: Derivatives of Vector-Valued Functions

In this worksheet, we will practice determining the derivatives of vector-valued functions and finding unit tangent vectors.

Q1:

Calculate , and find the vector form of the equation of the tangent line at for .

• A,
• B,
• C,
• D,
• E,

Q2:

Calculate , and find the vector form of the equation of the tangent line at for .

• A
• B
• C
• D
• E

Q3:

Calculate , and find the vector form of the equation of the tangent line at for .

• A,
• B,
• C,
• D,
• E,

Q4:

Consider the curve . Determine and find the tangent to the curve when .

• A,
• B,
• C,
• D,
• E,

Q5:

Given that , where and are constants, find .

• A
• B
• C
• D
• E

Q6:

Find the derivative of a vector-valued function .

• A
• B
• C
• D
• E

Q7:

Find the derivative of a vector-valued function .

• A
• B
• C
• D
• E

Q8:

Find the derivative of the vector-valued function .

• A
• B
• C
• D
• E

Q9:

Find the derivative of a vector-valued function .

• A
• B
• C
• D
• E

Q10:

Find the derivative of a vector-valued function .

• A
• B1
• C
• D
• E3

Q11:

Find the derivative of the following vector-valued function:

• A
• B
• C
• D
• E

Q12:

Find the derivative of the vector-valued function .

• A
• B
• C
• D
• E

Q13:

Find the derivative of the vector-valued function .

• A
• B
• C
• D
• E

Q14:

For the curve defined by the vector-valued equation , find the value of .

• A
• B
• C
• D
• E

Q15:

For the curve defined by the vector-valued equation , find the value of .

• A
• B
• C
• D
• E

Q16:

Calculate for the vector-valued functions and .

• A
• B
• C
• D
• E