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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derivative of

- \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}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \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}}

\int x \cdot ln (3 x) d x

\int 8 x d x

\frac{\partial}{\partial x} (x ln (x + 3 y))

\int \frac{- 4}{3 x ^{2}} d x

x \to 3 lim (\frac{x - 1}{3 - x})

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)