Find the Derivative of the Function $$y = \frac { x ^ { 2 } + 2 x - 2 } { x ^ { 2 } - 2 x + 2 }$$

question 260

Multiple Choice

Find the derivative of the function.
- $$y = \frac { x ^ { 2 } + 2 x - 2 } { x ^ { 2 } - 2 x + 2 }$$

• A) \(y ^ { \prime } = \frac { - 4 x ^ { 2 } - 8 x } { \left( x ^ { 2 } - 2 x + 2 \right) ^ { 2 } }\)
• B) \(y ^ { \prime } = \frac { - 4 x ^ { 2 } + 8 x } { \left( x ^ { 2 } - 2 x + 2 \right) ^ { 2 } }\)
• C) \(y ^ { \prime } = \frac { 4 x ^ { 2 } - 8 x } { \left( x ^ { 2 } - 2 x + 2 \right) ^ { 2 } }\)
• D) \(y ^ { \prime } = \frac { 4 x ^ { 2 } + 8 x } { \left( x ^ { 2 } - 2 x + 2 \right) ^ { 2 } }\)

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Definitions:

Simple Interest

Simple interest is a method of calculating the interest charge on a loan based on the original principal amount and the interest rate, without compounding.

Equivalent

Equal in value, amount, function, meaning, etc., often used in mathematics and chemistry.

Per Annum

A Latin term meaning "per year," often used in financial contexts to describe rates or amounts calculated over a yearly basis.

Invested

Invested refers to the allocation of resources, usually money, into a financial venture with the expectation of receiving future returns.