Calculus 1 : Other Differential Functions

Study concepts, example questions & explanations for Calculus 1

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Example Questions

Example Question #111 : Other Differential Functions

Find the differential of the following equation

Possible Answers:

Correct answer:

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.

Possible Answers:

Correct answer:

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.

Possible Answers:

Correct answer:

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

.

Possible Answers:

Correct answer:

Explanation:

Let .

Then .

By the chain rule,

Plugging everything in we get

 

Example Question #115 : Other Differential Functions

Let 

Find 

.

Possible Answers:

Correct answer:

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 

.

Possible Answers:

Correct answer:

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 

.

Possible Answers:

Correct answer:

Explanation:

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

.

Therefore,

.

Example Question #118 : Other Differential Functions

Let 

Find 

.

Possible Answers:

Correct answer:

Explanation:

Recall that, 

Using the product rule

Example Question #119 : Other Differential Functions

Compute the differential for the following.

Possible Answers:

Correct answer:

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.

Possible Answers:

Correct answer:

Explanation:

Using the power rule,

the derivative of  becomes .

Using trigonometric identities, the derivative of  is

Therefore, 

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