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GRE Subject Test: Math : Functions of More Than Two Variables

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

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Example Questions

Example Question #131 : Calculus

Solve for $\frac{\partial }{\partial x}$ : sx+x^2s^2+sxy

Possible Answers:

s+s^2+xy

s+2s^2x+sy

s+x+2sx^2+2s^2x

2s+2x+y+2sx^2+2s^2x

s+2s^2x

Correct answer:

s+2s^2x+sy

Explanation:

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

In sx+x^2s^2+sxy , the terms s, s^2, sy are constants.

Derive as accordingly by the differentiation rules.

$\frac{\partial }{\partial x}=s+2s^2x+sy$

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Example Question #132 : Calculus

Suppose the function $f=bcx+\frac{k}{c}+b^2ln(c)$ . Solve for $\frac{\partial f}{\partial c}$ .

Possible Answers:

$bx-\frac{k}{c^2}+\frac{b^2}{c}$

$c+\frac{1}{c}+ln(c)$

$bx+\frac{k}{c^2}+\frac{b^2}{c}$

$b+c+\frac{c-k}{c^2}+\frac{b^2}{c}+2b\cdot ln(c)$

$bx+b-\frac{k}{c^2}+\frac{b^2}{c}+2b\cdot ln(c)$

Correct answer:

$bx-\frac{k}{c^2}+\frac{b^2}{c}$

Explanation:

Identify all the constants in function $f=bcx+\frac{k}{c}+b^2ln(c)$ .

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

$\frac{\partial f}{\partial c}=bx-\frac{k}{c^2}+\frac{b^2}{c}$

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Example Question #1 : Partial Differentiation

Suppose the function $f=bcx+\frac{k}{c}+b^2ln(c)$ . Solve for $\frac{\partial f}{\partial c}$ .

Possible Answers:

$bx-\frac{k}{c^2}+\frac{b^2}{c}$

$b+c+\frac{c-k}{c^2}+\frac{b^2}{c}+2b\cdot ln(c)$

$bx+\frac{k}{c^2}+\frac{b^2}{c}$

$c+\frac{1}{c}+ln(c)$

$bx+b-\frac{k}{c^2}+\frac{b^2}{c}+2b\cdot ln(c)$

Correct answer:

$bx-\frac{k}{c^2}+\frac{b^2}{c}$

Explanation:

Identify all the constants in function $f=bcx+\frac{k}{c}+b^2ln(c)$ .

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

$\frac{\partial f}{\partial c}=bx-\frac{k}{c^2}+\frac{b^2}{c}$

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GRE Subject Test: Math : Functions of More Than Two Variables

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

All GRE Subject Test: Math Resources

Example Questions

Example Question #131 : Calculus

Example Question #132 : Calculus

Example Question #1 : Partial Differentiation

All GRE Subject Test: Math Resources

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