If $$ f(x)=7 e^{x}+x^{e} $$, find $$ f^{\prime}(x) $$. $$ \square $$

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1. Write the function:  
   $$
   f(x)=7e^{x}+x^{e}.
   $$

2. Differentiate the function term-by-term.

3. The derivative of the first term is:  
   $$
   \frac{d}{dx}\left(7e^{x}\right)=7e^{x}.
   $$

4. The derivative of the second term, using the power rule for $$ x^n $$ where $$ n $$ is a constant, is:  
   $$
   \frac{d}{dx}\left(x^{e}\right)=e\,x^{e-1}.
   $$

5. Therefore, the derivative of $$ f(x) $$ is:  
   $$
   f'(x)=7e^{x}+e\,x^{e-1}.
   $$
The derivative of $$ f(x) $$ is $$ f'(x) = 7e^{x} + e\,x^{e-1} $$.

If \( f(x)=7 e^{x}+x^{e} \), find \( f^{\prime}(x) \). \( \square \)

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