### All Calculus 1 Resources

## Example Questions

### Example Question #81 : Other Differential Functions

Find the derivative of the function

**Possible Answers:**

**Correct answer:**

To find the derivative of this function we must use the Chain Rule and the Quotient Rule. Applying the Chain Rule to the numerator gives

Now using the Quotient Rule for the function, we find the derivative to be

### Example Question #81 : Other Differential Functions

Find the derivative of

**Possible Answers:**

**Correct answer:**

To find the derivative of this function, we must use the Quotient Rule which is

Applying this to the function we are given, with and gives us

### Example Question #81 : How To Find Differential Functions

Find the derivative of the following function

**Possible Answers:**

**Correct answer:**

To find the derivative of this function we must use the Product Rule and the Quotient Rule. Appling the Product Rule to the numerator of the function gives us

Using this with the Quotient Rule, we find

### Example Question #84 : How To Find Differential Functions

Find the derivative of

**Possible Answers:**

**Correct answer:**

To find the derivative of this function we must use the Product Rule and the Chain Rule. If and then

Applying these derivatives to the Product Rule gives us

### Example Question #85 : How To Find Differential Functions

Differentiate:

**Possible Answers:**

**Correct answer:**

To find the derivative of this function we must use the Product Rule and the Chain Rule. First we set

and

Now differentiating both of these functions gives

Applying this to the Product Rule gives us,

### Example Question #86 : How To Find Differential Functions

Find the derivative of

**Possible Answers:**

None of these answers are correct.

**Correct answer:**

To find the derivative of this function we must use the Product Rule and the Chain Rule. If we have

and then

and

Applying this to the product rule, we find

### Example Question #87 : How To Find Differential Functions

Find the derivative of the function

**Possible Answers:**

None of these answers are correct.

**Correct answer:**

To find the derivative of this function, we must use the Product Rule, Quotient Rule, and the Chain Rule. To do this, we first find the derivative of each part.

Using the derivatives of each part we can find the derivative of the numerator using the Product Rule

Finally, putting this into the Quotient Rule gives

### Example Question #88 : How To Find Differential Functions

Differentiate the function

**Possible Answers:**

None of these answers are correct.

**Correct answer:**

To differentiate this function we must use the Quotient Rule

Using and .

The derivative of the function is then

### Example Question #89 : How To Find Differential Functions

Differentiate the following function

**Possible Answers:**

None of these answers are correct.

**Correct answer:**

To differentiate this function we must use the Chain Rule. where

Therefore the derivative of the function is

### Example Question #81 : Other Differential Functions

Find the derivative of the function

**Possible Answers:**

None of these answers are correct.

**Correct answer:**

To find the derivative of the function, we must use the Product Rule,

Using and .

Therefore

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