Differentiate: $f ( x ) = \frac { x ^ { 2 } } { x - 2 }$
A) $\frac { x ^ { 2 } - 4 x } { ( x - 2 ) ^ { 2 } }$
B) $\frac { 3 x ^ { 2 } + 4 x } { ( x - 2 ) ^ { 2 } }$
C) 2x
D) -x

Question

Quizplus · Accepted Answer

To differentiate $f(x) = \frac{x^2}{x-2}$, we use the quotient rule: $\left( \frac{u}{v} \right)' = \frac{u'v - uv'}{v^2}$, where $u = x^2$ and $v = x - 2$. Thus, $u' = 2x$ and $v' = 1$. Substituting these into the quotient rule formula gives $\frac{2x(x-2) - x^2(1)}{(x-2)^2} = \frac{2x^2 - 4x - x^2}{(x-2)^2} = \frac{x^2 - 4x}{(x-2)^2}$.

Differentiate f(x)=x2x−2f ( x ) = \frac { x ^ { 2 } } { x - 2 }f(x)=x−2x2​

Differentiate $f ( x ) = \frac { x ^ { 2 } } { x - 2 }$