If $f ( x ) = \left( x + 2 e ^ { - x } \right) ^ { 3 }$ , then $f ^ { \prime } ( x ) = 1 - 2 e ^ { - x }$ .

Question

Quizplus · Accepted Answer

The derivative $f'(x)$ of the given function $f(x) = (x + 2e^{-x})^3$ involves applying the chain rule and the product rule, and it does not simplify to $1 - 2e^{-x}$. The correct derivative would involve terms from the differentiation of both $x$ and $2e^{-x}$, and then multiplying by the derivative of the outer function, which would not simplify to $1 - 2e^{-x}$.

If f(x)=(x+2e−x)3f ( x ) = \left( x + 2 e ^ { - x } \right) ^ { 3 }f(x)=(x+2e−x)3

If $f ( x ) = \left( x + 2 e ^ { - x } \right) ^ { 3 }$