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

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

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

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

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

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

Solution steps

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

Simplify

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

= \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}}

\frac{d}{d x} (x^{4} y^{5} + 2 x m y (x)^{2} - 4 y^{3} a)

\int \frac{( 2 x + 4 )}{( x ^{2} + 5 x - 6 )} d x

\frac{d}{d x} ((x + y) (x - y))

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

\int \frac{1}{2 x ^{2} + 8 x + 20} d x

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