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Write the maximum value of f(x)=x^(1/...

Write the maximum value of `f(x)=x^(1//x)` .

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Let `f(x)=y=x^{1 / x}`
`\ln y=\frac{1}{x} \ln x `
`\frac{1}{y} \frac{d y}{d x}=\frac{1}{x^{2}}-\frac{1}{x^{2}} \ln x`
...
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