Derivative of $$$x^{e}$$$
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Your Input
Find $$$\frac{d}{dx} \left(x^{e}\right)$$$.
Solution
Apply the power rule $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ with $$$n = e$$$:
$${\color{red}\left(\frac{d}{dx} \left(x^{e}\right)\right)} = {\color{red}\left(e x^{-1 + e}\right)}$$Thus, $$$\frac{d}{dx} \left(x^{e}\right) = e x^{-1 + e}$$$.
Answer
$$$\frac{d}{dx} \left(x^{e}\right) = e x^{-1 + e}$$$A