What is the derivative of e^{-5/x} ?

The derivative of e^{-5/x} is (5e^{-5/x})/(x^2)

What is the first derivative of e^{-5/x} ?

The first derivative of e^{-5/x} is (5e^{-5/x})/(x^2)

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\frac{d}{d x} (e^{- \frac{5}{x}})

\frac{5 e ^{- \frac{5}{x}}}{x ^{2}}

Solution steps

\frac{d}{d x} (e^{- \frac{5}{x}})

Apply the chain rule:

e^{- \frac{5}{x}} \frac{d}{d x} (- \frac{5}{x})

= e^{- \frac{5}{x}} \frac{d}{d x} (- \frac{5}{x})

\frac{d}{d x} (- \frac{5}{x}) = \frac{5}{x ^{2}}

= e^{- \frac{5}{x}} \frac{5}{x ^{2}}

Multiply fractions:

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

= \frac{5 e ^{- \frac{5}{x}}}{x ^{2}}

\int x (3 x + 1) d x

n = 1 \sum \infty cos^{n} (0.8)

n = 0 \sum \infty n (\frac{5}{6})^{n - 1}

\frac{d}{d x} (x^{2} y + 3 x \cdot y^{3} + x)

\int cot (6 x) d x

What is the derivative of e^{-5/x} ?
The derivative of e^{-5/x} is (5e^{-5/x})/(x^2)
What is the first derivative of e^{-5/x} ?
The first derivative of e^{-5/x} is (5e^{-5/x})/(x^2)