Question
If \( f(x)=7 e^{x}+x^{e} \), find \( f^{\prime}(x) \). \( \square \)
Ask by Elliott Savage. in the United States
Mar 12,2025
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Answer
The derivative of \( f(x) \) is \( f'(x) = 7e^{x} + e\,x^{e-1} \).
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Mind Expander
To find the derivative of the function \( f(x)=7 e^{x}+x^{e} \), we can use the rules of differentiation. The derivative of \( e^x \) is \( e^x \), and the derivative of \( x^n \) is \( n x^{n-1} \). Thus, we calculate: 1. The derivative of \( 7 e^x \) is \( 7 e^x \). 2. The derivative of \( x^{e} \) is \( e x^{e-1} \). Combining these results, we get the derivative: \[ f^{\prime}(x) = 7 e^x + e x^{e-1}. \]