Calculus 1 : Other Differential Functions

Study concepts, example questions & explanations for Calculus 1

varsity tutors app store varsity tutors android store

Example Questions

Example Question #81 : Other Differential Functions

Find the derivative of the function

Possible Answers:

Correct answer:

Explanation:

To find the derivative of this function we must use the Chain Rule and the Quotient Rule. Applying the Chain Rule to the numerator gives

Now using the Quotient Rule for the function, we find the derivative to be

Example Question #81 : Other Differential Functions

Find the derivative of 

Possible Answers:

Correct answer:

Explanation:

To find the derivative of this function, we must use the Quotient Rule which is 

Applying this to the function we are given, with  and  gives us 

Example Question #81 : How To Find Differential Functions

Find the derivative of the following function

Possible Answers:

Correct answer:

Explanation:

To find the derivative of this function we must use the Product Rule and the Quotient Rule. Appling the Product Rule to the numerator of the function gives us

Using this with the Quotient Rule, we find 

Example Question #84 : How To Find Differential Functions

Find the derivative of 

Possible Answers:

Correct answer:

Explanation:

To find the derivative of this function we must use the Product Rule and the Chain Rule. If  and  then

Applying these derivatives to the Product Rule gives us

Example Question #85 : How To Find Differential Functions

Differentiate:

Possible Answers:

Correct answer:

Explanation:

To find the derivative of this function we must use the Product Rule and the Chain Rule. First we set 

and

Now differentiating both of these functions gives

Applying this to the Product Rule gives us,

 

Example Question #86 : How To Find Differential Functions

Find the derivative of 

Possible Answers:

None of these answers are correct.

Correct answer:

Explanation:

To find the derivative of this function we must use the Product Rule and the Chain Rule. If we have

 and  then

 and 

Applying this to the product rule, we find

 

Example Question #87 : How To Find Differential Functions

Find the derivative of the function

Possible Answers:

None of these answers are correct.

Correct answer:

Explanation:

To find the derivative of this function, we must use the Product Rule, Quotient Rule, and the Chain Rule. To do this, we first find the derivative of each part.

Using the derivatives of each part we can find the derivative of the numerator using the Product Rule

Finally, putting this into the Quotient Rule gives

Example Question #88 : How To Find Differential Functions

Differentiate the function

Possible Answers:

None of these answers are correct.

Correct answer:

Explanation:

To differentiate this function we must use the Quotient Rule

Using  and .

The derivative of the function is then

Example Question #89 : How To Find Differential Functions

Differentiate the following function

Possible Answers:

None of these answers are correct.

Correct answer:

Explanation:

To differentiate this function we must use the Chain Rule. where

Therefore the derivative of the function is

Example Question #81 : Other Differential Functions

Find the derivative of the function

Possible Answers:

None of these answers are correct.

Correct answer:

Explanation:

To find the derivative of the function, we must use the Product Rule, 

Using  and .

Therefore

Learning Tools by Varsity Tutors