Find the indicated derivative.
-$\frac { d t } { d x }$ if $t = \frac { x } { 2 x - 2 }$
A) $- \frac { 2 x } { ( 2 x - 2 ) ^ { 2 } }$
B) $- \frac { 2 } { ( 2 x - 2 ) ^ { 2 } }$
C) $\frac { 4 x - 2 } { ( 2 x - 2 ) ^ { 2 } }$
D) $- \frac { 2 } { 2 x - 2 }$

Question

Quizplus · Accepted Answer

To find the derivative $\frac{dt}{dx}$ of $t = \frac{x}{2x - 2}$, we can use the quotient rule: $\frac{d}{dx} \left( \frac{u}{v} \right) = \frac{u'v - uv'}{v^2}$, where $u = x$ and $v = 2x - 2$. Thus, $u' = 1$ and $v' = 2$. Substituting these into the quotient rule gives $\frac{dt}{dx} = \frac{(1)(2x - 2) - (x)(2)}{(2x - 2)^2} = \frac{2x - 2 - 2x}{(2x - 2)^2} = -\frac{2}{(2x - 2)^2}$.

Find the Indicated Derivative dtdx\frac { d t } { d x }dxdt​

Find the Indicated Derivative $\frac { d t } { d x }$