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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \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} (2 x - 9)

x \to 0 lim (4^{x})

\frac{s - 5}{( s ^{2} - 6 s + 25 )}

x^{4} - 4 x^{3} - 2, at x = 1

f (x) = 2 x e^{4 x}

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