Question

differentiate the following function: f(x)=e^x + x^e
attempt 2: 1 attempt remaining.
f(x)=
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Explanation:

Step1: Recall derivative rules

The derivative of $e^x$ is $e^x$ and the derivative of $x^n$ using the power - rule $\frac{d}{dx}(x^n)=nx^{n - 1}$. Here $n = e$.

Step2: Differentiate term - by - term

The derivative of $y = e^x+x^e$ is $\frac{d}{dx}(e^x)+\frac{d}{dx}(x^e)$.
Since $\frac{d}{dx}(e^x)=e^x$ and $\frac{d}{dx}(x^e)=ex^{e - 1}$, then $f'(x)=e^x+ex^{e - 1}$.

Answer:

$e^x+ex^{e - 1}$