Calculus 1 : Other Differential Functions

Study concepts, example questions & explanations for Calculus 1

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Example Questions

Example Question #121 : Other Differential Functions

Compute the differential for the following.

Possible Answers:

Correct answer:

Explanation:

To solve this problem, you must use the product rule of finding derivatives.

For any function , .

In this problem, the product rule yields 

.

Example Question #122 : Other Differential Functions

Calculate the differential for the following function.

Possible Answers:

Correct answer:

Explanation:

This differential can be found by utilizing the power rule,

.

The original equation is .

Using the power rule on each term we see that the derivative of  is . The derivative of a constant is always zero.

The dervative of  is

.

The derivative of  is

.

Thus, 

Multiply  to the right side to get the final solution. 

Example Question #123 : Other Differential Functions

Compute the following differential.

Possible Answers:

Correct answer:

Explanation:

Using the power rule, we can find the derivative of each part of the function. The power rule states to multiply the coefficient of the term by the exponent then decrease the exponent by one.

The derivative of  is .

The derivative of  is .

The derivative of  is .

And finally, because  is a constant, the derivative of  is .

Thus, when we add the parts together, the derivative is 

and

Example Question #124 : Other Differential Functions

Calculate the differential for the following function.

Possible Answers:

Correct answer:

Explanation:

To solve this problem, you may use the quotient rule for finding derivatives. The quotient rule stipulates that for a function 

,  .

In this problem,  and .

Thus, 

 

  

.

Therefore, 

 and .

Example Question #125 : Other Differential Functions

Calculate the differential of the following function.

Possible Answers:

Correct answer:

Explanation:

Using the power rule, we can find the derivative of each part of the function. When using the power rule you multiply the coefficient by the exponent then decrease the exponent by one.

The derivative of  is .

The derivative of  is .

The derivative of  is 

When these derivatives are added together, 

.

Thus, 

Example Question #126 : Other Differential Functions

Calculate the differential for the following function.

Possible Answers:

Correct answer:

Explanation:

Use the quotient rule to find this answer. The quotient rule dictates that for a function 

.

For this particular question,  and .

Apply the quotient rule to this function:

 

Example Question #127 : Other Differential Functions

Calculate the differential for the following function. 

Possible Answers:

Correct answer:

Explanation:

For finding the derivative of a root, it is helpful to turn the root into a power.

For example, in this problem it is helpful to turn the  into .

Now, we can easily apply the power rule,

which yields the answer 

.

 

 

Example Question #128 : Other Differential Functions

Calculate the differential for the following function.

Possible Answers:

Correct answer:

Explanation:

Using the power rule, we can solve this problem. The power rule states to multiply the coefficient with the exponent of the term then decrease the exponent by one.

The derivative of  is .

The derivative of  is .

Thus, 

 and 

Example Question #129 : Other Differential Functions

Calculate the differential for the following.

Possible Answers:

Correct answer:

Explanation:

Use the power rule to differentiate this function. The power rule states to multiply the coefficient by the exponent then decrease the exponent by one.

The derivative of  is .

The derivative of  is .

The derivative of  is .

Thus, 

 and 

Example Question #130 : Other Differential Functions

Calculate the differential for the following.

Possible Answers:

Correct answer:

Explanation:

Use the quotient rule to find the solution to this problem. The quotient rule stipulates that for a function 

In this problem,  and .

Apply the quotient rule: 

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