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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

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

Simplify

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

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

\int (sin (x))^{6} (cos (x))^{3} d x

\int sec^{6} (4 x) d x

f (x) = (3 x^{3} - 4 x^{2} + 5 x - 9)^{2}, at x = 2

x \to 2 lim (x^{2} + 6 x + 5)

x \to 0 + lim (x^{13 x})

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