Calculus 1 : Other Differential Functions

Study concepts, example questions & explanations for Calculus 1

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Example Questions

Example Question #101 : Other Differential Functions

Differentiate the trigonometric function.

Possible Answers:

Correct answer:

Explanation:

We can use the chain rule to differentiate, which states we will need to multiply the derivative of the outside function by the derivative of the inside function. We find the derivative of the inside function, , to be . The derivative of the outside function , will be . Multiplying these values together results in .

Example Question #102 : Other Differential Functions

Find the differential of the following equation.

Possible Answers:

Correct answer:

Explanation:

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

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

 

Example Question #102 : 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  is  and anything in the form of  is , so applying that rule to all of the terms yields:

 

Example Question #103 : 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 quotient rule.

The quotient rule is:

 ,

so applying that rule to the equation yields: 

Example Question #104 : 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 as follows.

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

 

Example Question #105 : 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  is , and derivative of anything in the form of  is , so applying that rule to all of the terms yields:

 

Example Question #106 : 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 #107 : 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 #108 : 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 [correct answer]:

Example Question #109 : 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 is , and the derivative of  is , so applying that rule to all of the terms yields [correct answer]:

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