Find the derivative of the following function using the limiting process. $$f ( x ) = \frac { 2 } { x - 3 }$$
A) $f ^ { t } ( x ) = \frac { 2 } { ( x + 3 ) ^ { 2 } }$
B) $f ^ { t } ( x ) = - \frac { 2 x } { ( x - 3 ) ^ { 2 } }$
C) $f ^ { t} ( x ) = - \frac { 2 } { ( x - 3 ) ^ { 2 } }$
D) $f ^ { t } ( x ) = \frac { 2 } { ( x - 3 ) ^ { 2 } }$
E) $f ^ { t } ( x ) = - \frac { 2 } { ( x + 3 ) ^ { 2 } }$

Question

Quizplus · Accepted Answer

The derivative of $f(x) = \frac{2}{x-3}$ using the quotient rule or the definition of the derivative via the limiting process results in $f'(x) = -\frac{2}{(x-3)^2}$. This is because the derivative of the denominator, when applied in the chain rule, introduces a negative sign, and the square of the denominator in the derivative formula results in $(x-3)^2$ in the denominator.

Find the Derivative of the Following Function Using the Limiting f(x)=2x−3f ( x ) = \frac { 2 } { x - 3 }f(x)=x−32​

Find the Derivative of the Following Function Using the Limiting $f ( x ) = \frac { 2 } { x - 3 }$