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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (ln ∣ tan (x) ∣)

\frac{1}{x + 1}, \frac{( x - 1 )}{2}, 0, 4

\frac{d}{d x} (3 x^{x})

x y + y^{^{'}} = 92 x

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

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