All Calculus 2 Resources
Example Questions
Example Question #1301 : Calculus Ii
Calculate the derivative of at the point .
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 .
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 .
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 .
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 .
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 .
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 .
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 .
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 .
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 :
The derivative of the function is
and was found using the following rules:
,
,
Evaluated at the point x=0, we get
.
Certified Tutor