Each of the following is a derivative of a function obtained by using the Quotient Rule. Determine the original function:
(a) $f ^ { \prime } ( x ) = \frac { ( x + 3 ) - ( x + 1 ) } { ( x + 3 ) ^ { 2 } }$ (b) $g ^ { \prime } ( x ) = \frac { 3 x ^ { 2 } e ^ { x } - x ^ { 3 } e ^ { x } } { e ^ { 2 x } }$ (c) $h ^ { \prime } ( x ) = \frac { x ^ { 3 } e ^ { x } - 3 x ^ { 2 } e ^ { x } } { x ^ { 6 } }$

Question

Quizplus · Accepted Answer

The Answer of Each of the following is a derivative of a function obtained by using the Quotient Rule. Determine the original function:
(a) $f ^ { \prime } ( x ) = \frac { ( x + 3 ) - ( x + 1 ) } { ( x + 3 ) ^ { 2 } }$ (b) $g ^ { \prime } ( x ) = \frac { 3 x ^ { 2 } e ^ { x } - x ^ { 3 } e ^ { x } } { e ^ { 2 x } }$ (c) $h ^ { \prime } ( x ) = \frac { x ^ { 3 } e ^ { x } - 3 x ^ { 2 } e ^ { x } } { x ^ { 6 } }$

Each of the Following Is a Derivative of a Function f′(x)=(x+3)−(x+1)(x+3)2f ^ { \prime } ( x ) = \frac { ( x + 3 ) - ( x + 1 ) } { ( x + 3 ) ^ { 2 } }f′(x)=(x+3)2(x+3)−(x+1)​

Each of the Following Is a Derivative of a Function $f ^ { \prime } ( x ) = \frac { ( x + 3 ) - ( x + 1 ) } { ( x + 3 ) ^ { 2 } }$