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}}

\frac{d}{d x} (x^{3} + x^{5})

\frac{d}{d x} (- 5 cot (x) + 3 sec (x))

\int \frac{x}{2 - x ^{2}} d x

x \to \infty lim (7 x - 3)

\frac{\partial}{\partial x} (\frac{x ^{2}}{x ^{2} + 1})

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)