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) $y ^ { \prime } = \frac { - 4 x ^ { 2 } - 8 x } { \left( x ^ { 2 } - 2 x + 2 \right) ^ { 2 } }$

Question

Quizplus · Accepted Answer

To find the derivative of the given function, we use the quotient rule: $(\frac{u}{v})' = \frac{u'v - uv'}{v^2}$, where $u = x^2 + 2x - 2$ and $v = x^2 - 2x + 2$. Differentiating $u$ and $v$ gives $u' = 2x + 2$ and $v' = 2x - 2$. Substituting these into the quotient rule formula and simplifying yields the correct answer.

Find the Derivative of the Function y=x2+2x−2x2−2x+2y = \frac { x ^ { 2 } + 2 x - 2 } { x ^ { 2 } - 2 x + 2 }y=x2−2x+2x2+2x−2​

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