What is the derivative of e^{1/x}-(e^{1/x}/x) ?

The derivative of e^{1/x}-(e^{1/x}/x) is (e^{1/x})/(x^3)

What is the first derivative of e^{1/x}-(e^{1/x}/x) ?

The first derivative of e^{1/x}-(e^{1/x}/x) is (e^{1/x})/(x^3)

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\frac{d}{d x} (e^{\frac{1}{x}} - \frac{e ^{\frac{1}{x}}}{x})

\frac{e ^{\frac{1}{x}}}{x ^{3}}

Solution steps

\frac{d}{d x} (e^{\frac{1}{x}} - \frac{e ^{\frac{1}{x}}}{x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (e^{\frac{1}{x}}) - \frac{d}{d x} (\frac{e ^{\frac{1}{x}}}{x})

\frac{d}{d x} (e^{\frac{1}{x}}) = - \frac{e ^{\frac{1}{x}}}{x ^{2}}

\frac{d}{d x} (\frac{e ^{\frac{1}{x}}}{x}) = \frac{- e ^{\frac{1}{x}} - e ^{\frac{1}{x}} x}{x ^{3}}

= - \frac{e ^{\frac{1}{x}}}{x ^{2}} - \frac{- e ^{\frac{1}{x}} - e ^{\frac{1}{x}} x}{x ^{3}}

Simplify

- \frac{e ^{\frac{1}{x}}}{x ^{2}} - \frac{- e ^{\frac{1}{x}} - e ^{\frac{1}{x}} x}{x ^{3}} : \frac{e ^{\frac{1}{x}}}{x ^{3}}

= \frac{e ^{\frac{1}{x}}}{x ^{3}}

What is the derivative of e^{1/x}-(e^{1/x}/x) ?
The derivative of e^{1/x}-(e^{1/x}/x) is (e^{1/x})/(x^3)
What is the first derivative of e^{1/x}-(e^{1/x}/x) ?
The first derivative of e^{1/x}-(e^{1/x}/x) is (e^{1/x})/(x^3)