The correct option is A y=x^1/x⇒ log y nbsp; =log x/x⇒y_1/y nbsp; =1 log x/x^2 nbsp; nbsp;= y.1 log x/x^2 nbsp;= x^1/x.1 log x/x^2 ...

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Derivative of Standard Functions

d/dx{ x^1/x}=...

Question

$\frac{d}{d x} {x^{1 / x}} =$

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1+logx

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Solution

The correct option is B

$y = x^{\frac{1}{x}} \Rightarrow l o g y$
$= \frac{l o g x}{x} \Rightarrow \frac{y_{1}}{y}$
$= \frac{1 - l o g x}{x^{2}}$
$= y . \frac{1 - l o g x}{x^{2}}$
$= x^{1 / x} . \frac{1 - l o g x}{x^{2}}$

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