GRE Subject Test: Math : Quotient Rule

Study concepts, example questions & explanations for GRE Subject Test: Math

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Example Questions

Example Question #1 : Quotient Rule

Find :  

Possible Answers:

Correct answer:

Explanation:

Write the quotient rule.

For the function  and ,  and .

Substitute and solve for the derivative.

 

Reduce the first term.

Example Question #2 : Quotient Rule

Find the following derivative:

Given 

Possible Answers:

Correct answer:

Explanation:

This question asks us to find the derivative of a quotient. Use the quotient rule:

Start by finding  and .

So we get:

Whew, let's simplify

Example Question #2 : Quotient Rule

Find derivative .

Possible Answers:

Correct answer:

Explanation:

This question yields to application of the quotient rule:

 

So find  and  to start:

So our answer is:

Example Question #11 : Finding Derivatives

Find the derivative of: .

Possible Answers:

None of the Above

Correct answer:

Explanation:

Step 1: We need to define the quotient rule. The quotient rule says: , where  is the derivative of  and  is the derivative of 

Step 2: We need to review how to take derivatives of different kinds of terms. When we are taking the derivative of terms in a polynomial, we need to follow these rules:

Rule 1: For any term with an exponent, the derivative of that term says: Drop the exponent and multiply it to the coefficient of that term. The new exponent of the derivative is  lower than the previous exponent. 

Example: 

Rule 2: For any term in the form , the derivative of that term is just , the coefficient of that term.

Ecample: 

Rule 3: The derivative of any constant is always 

Step 3: Find  and :




Step 4: Plug in all equations into the quotient rule:



Step 5: Simplify the fraction in step 4:



Step 6: Combine terms in the numerator in step 5:

.

The derivative of  is 

Example Question #3 : Quotient Rule

Find the derivative of: 

Possible Answers:

Correct answer:

Explanation:

Step 1: Define .



Step 2: Find .



Step 3: Plug in the functions/values into the formula for quotient rule: 



The derivative of the expression is 

Example Question #13 : Finding Derivatives

Find the second derivative of: 

Possible Answers:

None of the Above

Correct answer:

None of the Above

Explanation:

Finding the First Derivative:

Step 1: Define 



Step 2: Find 



Step 3: Plug in all equations into the quotient rule formula: 



Step 4: Simplify the fraction in step 3:






Step 5: Factor an  out from the numerator and denominator. Simplify the fraction..



We have found the first derivative..

Finding Second Derivative:

Step 6: Find  from the first derivative function



Step 7: Find 



Step 8: Plug in the expressions into the quotient rule formula: 

Step 9: Simplify:

 

I put "..." because the numerator is very long. I don't want to write all the terms...

 

Step 10: Combine like terms:



Step 11: Factor out  and simplify:

Final Answer: .

 

This is the second derivative.


The answer is None of the Above. The second derivative is not in the answers...

Example Question #14 : Finding Derivatives

Find derivative .

Possible Answers:

Correct answer:

Explanation:

This question yields to application of the quotient rule:

 

So find  and  to start:

So our answer is:

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