Calculate $\frac { \mathrm { d } y } { \mathrm {~d} x }$ . You need not expand your answer. $y = \frac { 2 x + 2 } { 4 x - 5 }$
A) $\frac { 2 ( 4 x - 5 ) + 4 ( 2 x + 2 ) } { 4 x - 5 }$
B) $\frac { 2 ( 4 x - 5 ) - 4 ( 2 x + 2 ) } { ( 4 x - 5 ) ^ { 2 } }$
C) $\frac { 2 ( 4 x - 5 ) + 4 ( 2 x + 2 ) } { ( 4 x - 5 ) ^ { 2 } }$
D) $2 ( 4 x - 5 ) - 4 ( 2 x + 2 )$
E) 0.5

Question

Calculate $\frac { \mathrm { d } y } { \mathrm {~d} x }$ . You need not expand your answer.  $y = \frac { 2 x + 2 } { 4 x - 5 }$ 
A) $\frac { 2 ( 4 x - 5 ) + 4 ( 2 x + 2 ) } { 4 x - 5 }$
B) $\frac { 2 ( 4 x - 5 ) - 4 ( 2 x + 2 ) } { ( 4 x - 5 ) ^ { 2 } }$
C) $\frac { 2 ( 4 x - 5 ) + 4 ( 2 x + 2 ) } { ( 4 x - 5 ) ^ { 2 } }$
D) $2 ( 4 x - 5 ) - 4 ( 2 x + 2 )$
E) 0.5

Quizplus · Accepted Answer

To find the derivative of $y = \frac { 2 x + 2 } { 4 x - 5 }$, we use the quotient rule: $\frac{d}{dx} \left( \frac{u}{v} \right) = \frac{u'v - uv'}{v^2}$, where $u = 2x + 2$ and $v = 4x - 5$. Differentiating $u$ and $v$ with respect to $x$ gives $u' = 2$ and $v' = 4$. Substituting these into the quotient rule formula gives $\frac{2(4x - 5) - 4(2x + 2)}{(4x - 5)^2}$, which matches option B.

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