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

question 246

Essay

Each of the following is a derivative of a function obtained by using the Product Rule. Determine the original function:
(a) $f ^ { \prime } ( x ) = 2 x e ^ { x } + x ^ { 2 } e ^ { x }$ (b) $g ^ { \prime } ( x ) = - 6 x \left( 5 x ^ { 3 } - 2 x \right) + \left( 1 - 3 x ^ { 2 } \right) \left( 15 x ^ { 2 } - 2 \right)$

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