What is the derivative of (e^{1/x}/(x^2)) ?

The derivative of (e^{1/x}/(x^2)) is (-e^{1/x}-2e^{1/x}x)/(x^4)

What is the first derivative of (e^{1/x}/(x^2)) ?

The first derivative of (e^{1/x}/(x^2)) is (-e^{1/x}-2e^{1/x}x)/(x^4)

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

\frac{- e ^{\frac{1}{x}} - 2 e ^{\frac{1}{x}} x}{x ^{4}}

Solution steps

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

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

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

\frac{d}{d x} (x^{2}) = 2 x

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

Simplify

\frac{( - \frac{e ^{\frac{1}{x}}}{x ^{2}} ) x ^{2} - 2 x e ^{\frac{1}{x}}}{( x ^{2} ) ^{2}} : \frac{- e ^{\frac{1}{x}} - 2 e ^{\frac{1}{x}} x}{x ^{4}}

= \frac{- e ^{\frac{1}{x}} - 2 e ^{\frac{1}{x}} x}{x ^{4}}

What is the derivative of (e^{1/x}/(x^2)) ?
The derivative of (e^{1/x}/(x^2)) is (-e^{1/x}-2e^{1/x}x)/(x^4)
What is the first derivative of (e^{1/x}/(x^2)) ?
The first derivative of (e^{1/x}/(x^2)) is (-e^{1/x}-2e^{1/x}x)/(x^4)