All Calculus 1 Resources
Example Questions
Example Question #731 : Other Differential Functions
Find the derivative:
Answer not listed
If , then the derivative is .
If , then the derivative is .
If , then the derivative is .
If , the the derivative is .
If , then the derivative is .
There are many other rules for the derivatives for trig functions.
If , then the derivative is . This is known as the chain rule.
In this case, we must find the derivative of the following:
That is done by doing the following:
Therefore, the answer is:
Example Question #732 : Other Differential Functions
Find the derivative:
Answer not listed
If , then the derivative is .
If , then the derivative is .
If , then the derivative is .
If , the the derivative is .
If , then the derivative is .
There are many other rules for the derivatives for trig functions.
If , then the derivative is . This is known as the chain rule.
In this case, we must find the derivative of the following:
That is done by doing the following:
Therefore, the answer is:
Example Question #732 : Other Differential Functions
Find the derivative.
Use the power rule to find the derivative.
Thus, the derivative is .
Example Question #733 : Other Differential Functions
Find the derivative:
Answer not listed
If , then the derivative is .
If , then the derivative is .
If , then the derivative is .
If , the the derivative is .
If , then the derivative is .
There are many other rules for the derivatives for trig functions.
If , then the derivative is . This is known as the chain rule.
In this case, we must find the derivative of the following:
That is done by doing the following:
Therefore, the answer is:
Example Question #922 : Differential Functions
Find the derivative:
Answer not listed
If , then the derivative is .
If , then the derivative is .
If , then the derivative is .
If , the the derivative is .
If , then the derivative is .
There are many other rules for the derivatives for trig functions.
If , then the derivative is . This is known as the chain rule.
In this case, we must find the derivative of the following:
That is done by doing the following:
Therefore, the answer is:
Example Question #923 : Differential Functions
Find the derivative:
Answer not listed
If , then the derivative is .
If , then the derivative is .
If , then the derivative is .
If , the the derivative is .
If , then the derivative is .
There are many other rules for the derivatives for trig functions.
If , then the derivative is . This is known as the chain rule.
In this case, we must find the derivative of the following:
That is done by doing the following:
Therefore, the answer is:
Example Question #924 : Differential Functions
Find the derivative:
Answer not listed
If , then the derivative is .
If , then the derivative is .
If , then the derivative is .
If , the the derivative is .
If , then the derivative is .
There are many other rules for the derivatives for trig functions.
If , then the derivative is . This is known as the chain rule.
In this case, we must find the derivative of the following:
That is done by doing the following:
Therefore, the answer is:
Example Question #925 : Differential Functions
Find the derivative:
Answer not listed
If , then the derivative is .
If , then the derivative is .
If , then the derivative is .
If , the the derivative is .
If , then the derivative is .
There are many other rules for the derivatives for trig functions.
If , then the derivative is . This is known as the chain rule.
In this case, we must find the derivative of the following:
That is done by doing the following:
Therefore, the answer is:
Example Question #926 : Differential Functions
Find the derivative:
Answer not listed
If , then the derivative is .
If , then the derivative is .
If , then the derivative is .
If , the the derivative is .
If , then the derivative is .
There are many other rules for the derivatives for trig functions.
If , then the derivative is . This is known as the chain rule.
In this case, we must find the derivative of the following:
That is done by doing the following:
Therefore, the answer is:
Example Question #927 : Differential Functions
Let on the interval . Find a value for the number(s) that satisfies the mean value theorem for this function and interval.
The mean value theorem states that for a planar arc passing through a starting and endpoint , there exists at a minimum one point, , within the interval for which a line tangent to the curve at this point is parallel to the secant passing through the starting and end points.
In other words, if one were to draw a straight line through these start and end points, one could find a point on the curve where the tangent would have the same slope as this line.
Note that the value of the derivative of a function at a point is the function's slope at that point; i.e. the slope of the tangent at said point.
First, find the two function values of Let on the interval
Then take the difference of the two and divide by the interval.
Now find the derivative of the function; this will be solved for the value(s) found above.
Using a calculator, we find the solution , which fits within the interval , satisfying the mean value theorem.
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