### All Calculus 1 Resources

## Example Questions

### Example Question #111 : Other Differential Functions

Find the differential of the following equation

**Possible Answers:**

**Correct answer:**

The differential of is .

To find the differential of the right side of the equation, take the derivative of each term as you apply the product rule.

The product rule is:

, so applying that rule to the equation yields:

### Example Question #112 : Other Differential Functions

Find the differential of the following equation.

**Possible Answers:**

**Correct answer:**

The differential of is .

To find the differential of the right side of the equation, take the derivative of each term as you apply the product rule.

The product rule is:

, so applying that rule to the equation yields:

### Example Question #113 : Other Differential Functions

Find the differential of the following equation.

**Possible Answers:**

**Correct answer:**

The differential of is .

To find the differential of the right side of the equation, take the derivative of each term as follows.

The derivative of anything in the form of is , and the derivative of is so applying that rule to all of the terms yields:

### Example Question #114 : Other Differential Functions

Find

.

**Possible Answers:**

**Correct answer:**

Let .

Then .

By the chain rule,

,

Plugging everything in we get

### Example Question #115 : Other Differential Functions

Let

Find

.

**Possible Answers:**

**Correct answer:**

Let and .

So .

By the product rule:

Where and .

Therefore,

Plugging everything in and simplifying we get:

### Example Question #116 : Other Differential Functions

Let

Find

.

**Possible Answers:**

**Correct answer:**

We can simplify the function by using the properties of logarithms.

With the simplified form, we can now find the derivative using the power rule which states,

.

Also we will need to use the product rule which is,

.

Remember that the derivative of .

Applying these rules we find the derivative to be as follows.

### Example Question #117 : Other Differential Functions

Let .

Find

.

**Possible Answers:**

**Correct answer:**

For a function of the form the derivative is by definition:

.

Therefore,

.

### Example Question #118 : Other Differential Functions

Let

Find

.

**Possible Answers:**

**Correct answer:**

Recall that,

Using the product rule

### Example Question #119 : Other Differential Functions

Compute the differential for the following.

**Possible Answers:**

**Correct answer:**

To compute the differential of the function we will need to use the power rule which states,

.

Applying the power rule we get:

From here solve for dy:

### Example Question #120 : Other Differential Functions

Compute the differential for the following function.

**Possible Answers:**

**Correct answer:**

Using the power rule,

the derivative of becomes .

Using trigonometric identities, the derivative of is .

Therefore,

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