Calculus 2 : Derivative at a Point

Study concepts, example questions & explanations for Calculus 2

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Example Questions

Example Question #91 : Derivative At A Point

Calculate the derivative of  at the point .

Possible Answers:

Correct answer:

Explanation:

There are 2 steps to solving this problem.

First, take the derivative of 

Then, replace the value of x with the given point and evaluate

For example, if  , then we are looking for the value of  , or the derivative of  at .

Calculate 

Derivative rules that will be needed here:

  • Derivative of a constant is 0. For example, 
  • Taking a derivative on a term, or using the power rule, can be done by doing the following:

Then, plug in the value of x and evaluate

Example Question #1292 : Calculus Ii

Calculate the derivative of  at the point .

Possible Answers:

Correct answer:

Explanation:

There are 2 steps to solving this problem.

First, take the derivative of 

Then, replace the value of x with the given point and evaluate

For example, if  , then we are looking for the value of  , or the derivative of  at .

Calculate 

Derivative rules that will be needed here:

  • Derivative of a constant is 0. For example, 
  • Taking a derivative on a term, or using the power rule, can be done by doing the following:

Then, plug in the value of x and evaluate

Example Question #91 : Derivative At A Point

Calculate the derivative of  at the point .

Possible Answers:

Correct answer:

Explanation:

There are 2 steps to solving this problem.

First, take the derivative of 

Then, replace the value of x with the given point and evaluate

For example, if  , then we are looking for the value of  , or the derivative of  at .

Calculate 

Derivative rules that will be needed here:

  • Derivative of a constant is 0. For example, 
  • Taking a derivative on a term, or using the power rule, can be done by doing the following: 

Then, plug in the value of x and evaluate

Example Question #1301 : Calculus Ii

Calculate the derivative of  at the point .

Possible Answers:

Correct answer:

Explanation:

There are 2 steps to solving this problem.

First, take the derivative of 

Then, replace the value of x with the given point and evaluate

For example, if  , then we are looking for the value of , or the derivative of  at .

Derivative rules that will be needed here:

  • Derivative of a constant is 0. For example, 
  • 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.

Calculate .

Then, plug in the value of x and evaluate.

 

 

Example Question #1301 : Calculus Ii

Calculate the derivative of  at the point .

Possible Answers:

Correct answer:

Explanation:

There are 2 steps to solving this problem.

First, take the derivative of 

Then, replace the value of x with the given point and evaluate

For example, if  , then we are looking for the value of  , or the derivative of  at .

Derivative rules that will be needed here:

  • When differentiating an exponential function:  , where k is a constant.

 

Calculate .

Then, plug in the value of x and evaluate.

 

 

Example Question #1302 : Calculus Ii

Calculate the derivative of  at the point .

Possible Answers:

Correct answer:

Explanation:

There are 2 steps to solving this problem.

First, take the derivative of 

Then, replace the value of x with the given point and evaluate

For example, if  , then we are looking for the value of  , or the derivative of  at .

Calculate .

Derivative rules that will be needed here:

  • When differentiating an exponential function: , where k is a constant.

Then, plug in the value of x and evaluate.

Example Question #1303 : Calculus Ii

Calculate the derivative of +x at the point .

Possible Answers:

Correct answer:

Explanation:

There are 2 steps to solving this problem.

First, take the derivative of 

Then, replace the value of x with the given point and evaluate

For example, if  , then we are looking for the value of  , or the derivative of  at .

Calculate 

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.

Then, plug in the value of x and evaluate.

 

 

 

Example Question #92 : Derivative At A Point

Calculate the derivative of  at the point .

Possible Answers:

Correct answer:

Explanation:

There are 2 steps to solving this problem.

First, take the derivative of 

Then, replace the value of x with the given point and evaluate

For example, if  , then we are looking for the value of  , or the derivative of  at .

Calculate 

Derivative rules that will be needed here:

Then, plug in the value of x and evaluate.

 

 

Example Question #181 : Derivative Review

Calculate the derivative of  at the point .

Possible Answers:

Correct answer:

Explanation:

There are 2 steps to solving this problem.

First, take the derivative of .

Then, replace the value of x with the given point and evaluate.

For example, if  , then we are looking for the value of  , or the derivative of  at .

Calculate .

Derivative rules that will be needed here:

Then, plug in the value of x and evaluate.

 

 

 

Example Question #181 : Derivative Review

Calculate the derivative of  at the point .

Possible Answers:

Correct answer:

Explanation:

There are 2 steps to solving this problem.

First, take the derivative of .

Then, replace the value of x with the given point and evaluate.

For example, if  , then we are looking for the value of  , or the derivative of  at .

 

Calculate 

Derivative rules that will be needed here:

 

 

Then, plug in the value of x and evaluate.

 

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