Functions of More Than Two Variables

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GRE Quantitative Reasoning › Functions of More Than Two Variables

Questions 1 - 3

1

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

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

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

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

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

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

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.

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

2

Solve for $\frac{\partial }{\partial x}$ :

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.

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

3

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

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

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

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

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

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

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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