### All AP Calculus AB Resources

## Example Questions

### Example Question #61 : Chain Rule And Implicit Differentiation

Given the function , find its derivative.

**Possible Answers:**

**Correct answer:**

Given the function , we can find its derivative using the chain rule, which states that

where and for . We have and , which gives us

### Example Question #62 : Chain Rule And Implicit Differentiation

Given the function , find its derivative.

**Possible Answers:**

**Correct answer:**

Given the function , we can find its derivative using the chain rule, which states that

where and for . We have and , which gives us

### Example Question #63 : Chain Rule And Implicit Differentiation

Given the function , find its derivative.

**Possible Answers:**

**Correct answer:**

Given the function , we can find its derivative using the chain rule, which states that

where and for . We have and , which gives us

### Example Question #64 : Chain Rule And Implicit Differentiation

Given the function , find its derivative.

**Possible Answers:**

**Correct answer:**

Given the function , we can find its derivative using the chain rule, which states that

where and for . We have and , which gives us

### Example Question #65 : Chain Rule And Implicit Differentiation

Find .

**Possible Answers:**

**Correct answer:**

Let

Then

can be rewritten as

Let

The function can now be rewritten as

Applying the chain rule twice:

### Example Question #62 : Chain Rule And Implicit Differentiation

Find the derivative of the function

**Possible Answers:**

**Correct answer:**

To find the derivative of the function, you must apply the chain rule, which is as follows:

Using the function from the problem statement, we have that

and

Following the rule, we get

### Example Question #65 : Chain Rule And Implicit Differentiation

Find the derivative of the function

**Possible Answers:**

**Correct answer:**

To find the derivative of the function, you must apply the chain rule, which is as follows:

Using the function from the problem statement, we have that

and

Following the rule, we get

### Example Question #68 : Chain Rule And Implicit Differentiation

Find .

**Possible Answers:**

None of the other choices gives the correct response.

**Correct answer:**

Let

Then

and

Apply the chain rule:

Substitute back for :

Apply the sum rule:

After some simple algebra:

### Example Question #69 : Chain Rule And Implicit Differentiation

is a function of . Solve for in this differential equation:

**Possible Answers:**

**Correct answer:**

The expressions with can be separated from those with by multiplying both sides by :

Find the indefinite integral of both sides:

Set . Then , or , and

Substitute back:

;

Raise to both powers:

.

The correct choice is

### Example Question #70 : Chain Rule And Implicit Differentiation

Find the derivative using the chain rule.

**Possible Answers:**

**Correct answer:**

Use the chain rule to find the derivative:

Thus,

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