How do you find the derivative of $y = e^{\frac{1}{x}}$ $y=e^(1/x)$ ?

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How do you find the derivative of $y = e^{\frac{1}{x}}$ $y=e^(1/x)$ ?

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Answer 1 · 2014-07-30T20:00:08

$y'=-e^(1/x)/(x^2)$

Explanation :

Using Chain Rule,

Suppose, $y=e^f(x)$

then, $y'=e^f(x)*f'(x)$

Similarly following for the $y=e^(1/x)$

$y'=e^(1/x)*(1/x)'$

$y'=e^(1/x)*(-1/x^2)$

$y'=-e^(1/x)/(x^2)$

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How do you find the derivative of $y = e^{\frac{1}{x}}$ $y=e^(1/x)$ ?

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