All Calculus 2 Resources
Example Questions
Example Question #41 : Derivative At A Point
What is the slope of at ?
We define slope as the first derivative of a given function.
Since we have
, we can use the Power Rule
for all to determine that
.
We also have a point with a -coordinate , so the slope
.
Example Question #42 : Derivative At A Point
What is the slope of at ?
None of the above
We define slope as the first derivative of a given function.
Since we have
, we can use the Power Rule
for all to determine that
.
We also have a point with a -coordinate , so the slope
.
Example Question #43 : Derivative At A Point
What is the slope of at ?
None of the above
We define slope as the first derivative of a given function.
Since we have
, we can use the Power Rule
for all to determine that
.
We also have a point with a -coordinate , so the slope
.
Example Question #3 : Derivative Rules For Sums, Products, And Quotients
Find the slope of the tangent line to the function at .
The slope of the tangent line to a function at a point is the value of the derivative of the function at that point. In this problem, is a quotient of two functions, , so the quotient rule is needed.
In general, the quotient rule is
.
To apply the quotient rule in this example, you must also know that and that .
Therefore, the derivative is
The last step is to substitute for in the derivative, which will tell us the slope of the tangent line to at .
Example Question #41 : Derivative At A Point
What is the slope of at the point ?
We define slope as the first derivative of a given function.
Since we have , we can use the Power Rule
for all to determine that
.
We also have a point with a -coordinate , so the slope
.
Example Question #45 : Derivative At A Point
What is the slope of at the point ?
We define slope as the first derivative of a given function.
Since we have , we can use the Power Rule
for all to determine that
.
We also have a point with a -coordinate , so the slope
.
Example Question #46 : Derivative At A Point
What is the slope of at the point ?
We define slope as the first derivative of a given function.
Since we have , we can use the Power Rule
for all to determine that
.
We also have a point with a -coordinate , so the slope
.
Example Question #47 : Derivative At A Point
Find the derivative of the following function at :
The derivative of the function is
and was found using the following rules:
, ,
where , , and
Simply plug in into the first derivative function and solve:
Example Question #41 : Derivative At A Point
What is the slope of a function at ?
We define slope as the first derivative of a given function.
Since we have
, we can use the Power Rule
for all to determine that
.
We also have a point with a -coordinate , so the slope
.
Example Question #49 : Derivative At A Point
What is the slope of a function at ?
We define slope as the first derivative of a given function.
Since we have
, we can use the Power Rule
for all to determine that
.
We also have a point with a -coordinate , so the slope
.
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