GRE Subject Test: Math : Partial Differentiation

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

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Example Questions

Example Question #1 : Implicit Differentiation

Differentiate the following with respect to 

Possible Answers:

Correct answer:

Explanation:

The first step is to differentiate both sides with respect to :

Note: Those that are functions of  can be differentiated with respect to , just remember to mulitply it by 

Now we can solve for :

Example Question #1 : Partial Differentiation

Find 

 for .

Possible Answers:

Correct answer:

Explanation:

Our first step would be to differentiate both sides with respect to :

The functions of  can be differentiated with respect to , just remember to multiply by  .

Example Question #21 : Derivatives & Integrals

Differentiate the following to solve for .

Possible Answers:

 

Correct answer:

 

Explanation:

Our first step is to differentiate both sides with respect to :

The functions of  can by differentiated with respect to , just remember to multiply them by 

Example Question #1 : Partial Differentiation

Differentiate the following with respect to .

Possible Answers:

Correct answer:

Explanation:

Our first step is to differentiate both sides with respect to :

Note: we can differentiate the terms that are functions of  with respect to , just remember to multiply it by .

Note: The product rule was applied above: 

Example Question #1 : Partial Differentiation

Solve for :  

 

Possible Answers:

Correct answer:

Explanation:

To solve for the partial derivative, let all other variables be constants besides the variable that is derived with respect to.

In , the terms  are constants.

Derive as accordingly by the differentiation rules.

 

 

Example Question #1 : Functions Of More Than Two Variables

Suppose the function .  Solve for .

Possible Answers:

Correct answer:

Explanation:

Identify all the constants in function .

Since we are solving for the partial differentiation of variable , all the other variables are constants.  Solve each term by differentiation rules.

Example Question #1 : Functions Of More Than Two Variables

Suppose the function .  Solve for .

Possible Answers:

Correct answer:

Explanation:

Identify all the constants in function .

Since we are solving for the partial differentiation of variable , all the other variables are constants.  Solve each term by differentiation rules.

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