# Calculus 1 : Other Differential Functions

## Example Questions

### Example Question #111 : Other Differential Functions

Find the differential of the following equation

Explanation:

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.

Explanation:

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.

Explanation:

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

.

Explanation:

Let .

Then .

By the chain rule,

Plugging everything in we get

### Example Question #115 : Other Differential Functions

Let

Find

.

Explanation:

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

.

Explanation:

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

.

Explanation:

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

.

Therefore,

.

### Example Question #118 : Other Differential Functions

Let

Find

.

Explanation:

Recall that,

Using the product rule

### Example Question #119 : Other Differential Functions

Compute the differential for the following.

Explanation:

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.