Calculus 2 : Calculus II

Study concepts, example questions & explanations for Calculus 2

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Example Questions

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 #1304 : 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:

Then, plug in the value of x and evaluate.

 

 

Example Question #97 : 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 : Derivatives

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 #101 : 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:

  • 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 #182 : Derivative Review

Determine the derivative of the following function at .

Possible Answers:

Correct answer:

Explanation:

For this function we will need to use the power rule, the exponential rule, and the chain rule.

Power Rule: 

Exponential Rule: 

Chain Rule: 

Applying these rules to our function we get the following derivative.

Now, plug in  to solve,

.

Example Question #183 : Derivative Review

Find the derivative of the following function at :

Possible Answers:

Correct answer:

Explanation:

The derivative of the function is

and was found using the following rules:

Evaluated at the point x=0, we get

.

 

 

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