Find the Differential Of $z = \frac { 1 } { x + y ^ { 2 } }$

question 249

Multiple Choice

Find the differential of $z = \frac { 1 } { x + y ^ { 2 } }$ at the point $( x , y ) = ( 1,1 )$ .

• A) \(- d x - d y\)
• B) \(- \frac { 1 } { 4 } d x - \frac { 1 } { 2 } d y\)
• C)\(- d x - \frac { 1 } { 2 } d y\)
• D)\(- \frac { 1 } { 2 } d x - d y\)
• E) \(d x + d y\)
• F) \(\frac { 1 } { 4 } d x + \frac { 1 } { 2 } d y\)
• G) \(d x + \frac { 1 } { 2 } d y\)
• H) \(\frac { 1 } { 2 } d x + d y\)

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Definitions:

At-risk Rules

These are tax rules designed to limit the amount of deductible losses from businesses or income-producing activities to the amount the taxpayer has at risk.

Passive Loss Rules

Tax regulations that limit the amount of losses investors can deduct from passive activities, including some investments in real estate.

Materially Participate

The level of involvement by a taxpayer in the operations of a business that is sufficient enough to qualify for tax deductions related to active participation.

At-risk Amount

The amount of money in a particular investment that can be claimed as a deduction in the event of a loss.