Calculus 2 : Derivatives of Vectors

Study concepts, example questions & explanations for Calculus 2

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Example Questions

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Example Question #31 : Derivatives Of Vectors

Possible Answers:

Correct answer:

Explanation:

In general:

If ,

then 

Derivative rules that will be needed here:

  • Taking a derivative on a term, or using the power rule, can be done by doing the following:
  • When taking derivatives of sums, evaluate with the sum rule which states that the derivative of the sum is the same as the sum of the derivative of each term: 
  • Special rule when differentiating an exponential function:  , where k is a constant.

In this problem, 

Put it all together to get 

 

Example Question #32 : Derivatives Of Vectors

Possible Answers:

Correct answer:

Explanation:

In general:

If ,

then 

Derivative rules that will be needed here:

  • Taking a derivative on a term, or using the power rule, can be done by doing the following:
  • Special rule when differentiating an exponential function:  , where k is a constant.

In this problem, 

Put it all together to get 

Example Question #31 : Derivatives Of Vectors

Possible Answers:

Correct answer:

Explanation:

In general:

If ,

then 

Derivative rules that will be needed here:

  • Taking a derivative on a term, or using the power rule, can be done by doing the following:

In this problem, 

Put it all together to get 

Example Question #32 : Derivatives Of Vectors

Possible Answers:

Correct answer:

Explanation:

In general:

If ,

then 

Derivative rules that will be needed here:

  • Special rule when differentiating an exponential function:  , where k is a constant.

In this problem, 

Put it all together to get 

Example Question #32 : Derivatives Of Vectors

Possible Answers:

Correct answer:

Explanation:

In general:

If ,

then 

Derivative rules that will be needed here:

  • Special rule when differentiating an exponential function: , where k is a constant.

In this problem, 

 

Put it all together to get 

Example Question #36 : Derivatives Of Vectors

Calculate 

Possible Answers:

Correct answer:

Explanation:

In general:

If ,

then 

Derivative rules that will be needed here:

  • Taking a derivative on a term, or using the power rule, can be done by doing the following:
  • When taking derivatives of sums, evaluate with the sum rule which states that the derivative of the sum is the same as the sum of the derivative of each term: 
  • Special rule when differentiating an exponential function:  , where k is a constant.

In this problem, 

Use the sum rule and the power rule on each of the components.

Put it all together to get 

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