What is the derivative of e^{-4/x} ?

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

What is the first derivative of e^{-4/x} ?

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

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\frac{d}{d x} (e^{- \frac{4}{x}})

\frac{4 e ^{- \frac{4}{x}}}{x ^{2}}

Solution steps

\frac{d}{d x} (e^{- \frac{4}{x}})

Apply the chain rule:

e^{- \frac{4}{x}} \frac{d}{d x} (- \frac{4}{x})

= e^{- \frac{4}{x}} \frac{d}{d x} (- \frac{4}{x})

\frac{d}{d x} (- \frac{4}{x}) = \frac{4}{x ^{2}}

= e^{- \frac{4}{x}} \frac{4}{x ^{2}}

Multiply fractions:

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

= \frac{4 e ^{- \frac{4}{x}}}{x ^{2}}

y^{^{'}} = \frac{6 x ^{4} + y ^{4}}{x y ^{3}}

\int \frac{7 x ^{2}}{5 - x ^{6}} d x

x = - 3, x = 1, y = e^{x}, y = 1 - e^{x}

x y^{^{'}} + y = e^{x}, y (1) = 3

x \to 0 lim (x^{2} sin (x^{2}))

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