AP Calculus BC : AP Calculus BC

Study concepts, example questions & explanations for AP Calculus BC

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Example Questions

Example Question #31 : First And Second Derivatives Of Functions

If , find  in terms of  and .

Possible Answers:

None of the other answers

Correct answer:

Explanation:

Using a combination of logarithms, implicit differentiation, and a bit of algebra, we have

. Quotient Rule + implicit differentiation.

Example Question #32 : First And Second Derivatives Of Functions

Find the derivative of the function 

Possible Answers:

None of the other answers

Correct answer:

None of the other answers

Explanation:

The correct answer is .

 

Using the Quotient Rule and the fact , we have

 

.

Example Question #11 : Derivative Rules For Sums, Products, And Quotients

Possible Answers:

Correct answer:

Explanation:

First, factor out . Now we can differentiate using the product rule, 

Here,  so  so 

The answer is 

Example Question #12 : Derivative Rules For Sums, Products, And Quotients

Possible Answers:

Correct answer:

Explanation:

According to the product rule, . Here  so  so 

The derivative is 

Factoring out the 2 gives . Remembering the double angle trigonometric identity finally gives 

Example Question #403 : Ap Calculus Bc

If , find 

Possible Answers:

Correct answer:

Explanation:

First, we need to find . We can do that by using the quotient rule.

.

Plugging  in for  and simplifying, we get

.

Example Question #404 : Ap Calculus Bc

Find the derivative of f:

Possible Answers:

Correct answer:

Explanation:

The derivative of the function is equal to

and was found using the following rules:

Example Question #405 : Ap Calculus Bc

Find the derivative of the function:

where  is a constant

Possible Answers:

Correct answer:

Explanation:

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 #406 : Ap Calculus Bc

Compute the first derivative of the following function.

Possible Answers:

Correct answer:

Explanation:

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

Next, let's tackle the second part

Now, combine the two to get:

Example Question #407 : Ap Calculus Bc

Evaluate the derivative of the function .

Possible Answers:

Correct answer:

Explanation:

Use the product rule:  

where  and .

By the power rule, 

By the chain rule, .

Therefore, the derivative of the entire function is:

.

Example Question #408 : Ap Calculus Bc

Find the second derivative of g(x)

Possible Answers:

Correct answer:

Explanation:

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:

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