All Calculus AB Resources
Example Questions
Example Question #31 :Calculus Ab
Find the slope of the tangent line to the functionat.
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 thatand that.
Therefore, the derivative is
The last step is to substituteforin the derivative, which will tell us the slope of the tangent line toat.
Example Question #32 :Calculus Ab
First, factor out:. Now we can differentiate using the product rule,.
Here,so.so.
The answer is
Example Question #31 :Limits And Continuity
According to the product rule,. Hereso.so.
The derivative is
Factoring out the 2 gives. Remembering the double angle trigonometric identity finally gives
Example Question #34 :Calculus Ab
If, find
First, we need to find. We can do that by using the quotient rule.
.
Pluggingin forand simplifying, we get
.
Example Question #35 :Calculus Ab
找到derivative of f:
The derivative of the function is equal to
and was found using the following rules:
,,,
Example Question #36 :Calculus Ab
找到derivative of the function:
whereis a constant
When taking the derivative of the sum, we simply take the derivative of each component.
The derivative of the function is
and was found using the following rules:
,
Example Question #37 :Calculus Ab
Compute the first derivative of the following function.
Compute the first derivative of the following function.
To solve this problem, we need to apply the product rule:
So, we need to apply this rule to each of the terms in our function. Let's start with the first term
接下来,让我们解决第二个问题part
Now, combine the two to get:
Example Question #31 :Limits And Continuity
Supposeandare differentiable functions, and.
Calculate the derivative of, at.
None of the other answers
None of the other answers
The correct answer is 11.
Taking the derivative ofinvolves the product rule, and the chain rule.
Substitutinginto both sides of the derivative we get
Example Question #39 :Calculus Ab
Find the second derivative of g(x)
Find the second derivative of g(x)
To find this derivative, we need to use the product rule:
So, let's begin:
So, we are closer, but we need to derive again to get the 2nd derivative
So, our answer is:
Example Question #40 :Calculus Ab
Evaluate the derivative of the function.
Use the product rule:
whereand.
By the power rule,.
By the chain rule,.
Therefore, the derivative of the entire function is:
.
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