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

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

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

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

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Popular >

\frac{d}{d x} (e^{- \frac{a}{x}})

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

Solution steps

\frac{d}{d x} (e^{- \frac{a}{x}})

Apply the chain rule:

e^{- \frac{a}{x}} \frac{d}{d x} (- \frac{a}{x})

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

x \to 3 lim (\frac{4 x - 12}{x - 3})

\int \frac{sin ( x )}{x} d x

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

\int tan^{3} (7 π x) d x

\frac{0.5 s}{5 s ^{2} + 10 s + 49}

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