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

The derivative of-x^{-2}e^{1/x} is (2e^{1/x})/(x^3)+(e^{1/x})/(x^4)

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

The first derivative of-x^{-2}e^{1/x} is (2e^{1/x})/(x^3)+(e^{1/x})/(x^4)

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derivative of

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

\frac{2 e ^{\frac{1}{x}}}{x ^{3}} + \frac{e ^{\frac{1}{x}}}{x ^{4}}

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{- 2}, g = e^{\frac{1}{x}}

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

\frac{d}{d x} (x^{- 2}) = - \frac{2}{x ^{3}}

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

= - ((- \frac{2}{x ^{3}}) e^{\frac{1}{x}} + (- \frac{e ^{\frac{1}{x}}}{x ^{2}}) x^{- 2})

Simplify

- ((- \frac{2}{x ^{3}}) e^{\frac{1}{x}} + (- \frac{e ^{\frac{1}{x}}}{x ^{2}}) x^{- 2}) : \frac{2 e ^{\frac{1}{x}}}{x ^{3}} + \frac{e ^{\frac{1}{x}}}{x ^{4}}

= \frac{2 e ^{\frac{1}{x}}}{x ^{3}} + \frac{e ^{\frac{1}{x}}}{x ^{4}}

5 + 4 x^{2} - 2 x^{3}

\frac{x}{8} - \frac{8}{x}

y^{^{''}} - 7 y^{^{'}} + 6 y = 0

\int \frac{y ^{3}}{y ^{2} + 1} d y

\frac{d}{d x} (a x cos (3 x) + b x sin (3 x))

What is the derivative of-x^{-2}e^{1/x} ?
The derivative of-x^{-2}e^{1/x} is (2e^{1/x})/(x^3)+(e^{1/x})/(x^4)
What is the first derivative of-x^{-2}e^{1/x} ?
The first derivative of-x^{-2}e^{1/x} is (2e^{1/x})/(x^3)+(e^{1/x})/(x^4)