If $f ( x ) = \left( x + 7 e ^ { - x } \right) ^ { 8 }$ , then $f ^ { \prime } ( x ) = x + 7 e ^ { - x }$ .

Name: If $f ( x ) = \left( x + 7 e ^ { - x } \right) ^ { 8 }$ , then $f ^ { \prime } ( x ) = x + 7 e ^ { - x }$ .
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The derivative $f'(x)$ of the given function $f(x) = (x + 7e^{-x})^8$ involves applying the chain rule, which would not simplify to $x + 7e^{-x}$, but rather to the derivative of the outer function times the derivative of the inner function, leading to a more complex expression.

If f(x)=(x+7e−x)8f ( x ) = \left( x + 7 e ^ { - x } \right) ^ { 8 }f(x)=(x+7e−x)8

If $f ( x ) = \left( x + 7 e ^ { - x } \right) ^ { 8 }$