### All GRE Subject Test: Math Resources

## Example Questions

### Example Question #1 : Implicit Differentiation

Differentiate the following with respect to .

**Possible Answers:**

**Correct answer:**

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:**

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:**

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:**

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:**

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:**

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:**

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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