What is the derivative of e^{-1/(x^7}) ?

The derivative of e^{-1/(x^7}) is (7e^{-1/(x^7)})/(x^8)

What is the first derivative of e^{-1/(x^7}) ?

The first derivative of e^{-1/(x^7}) is (7e^{-1/(x^7)})/(x^8)

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\frac{d}{d x} (e^{- \frac{1}{x ^{7}}})

\frac{7 e ^{- \frac{1}{x ^{7}}}}{x ^{8}}

Solution steps

\frac{d}{d x} (e^{- \frac{1}{x ^{7}}})

Apply the chain rule:

e^{- \frac{1}{x ^{7}}} \frac{d}{d x} (- \frac{1}{x ^{7}})

= e^{- \frac{1}{x ^{7}}} \frac{d}{d x} (- \frac{1}{x ^{7}})

\frac{d}{d x} (- \frac{1}{x ^{7}}) = \frac{7}{x ^{8}}

= e^{- \frac{1}{x ^{7}}} \frac{7}{x ^{8}}

Multiply fractions:

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

= \frac{7 e ^{- \frac{1}{x ^{7}}}}{x ^{8}}

What is the derivative of e^{-1/(x^7}) ?
The derivative of e^{-1/(x^7}) is (7e^{-1/(x^7)})/(x^8)
What is the first derivative of e^{-1/(x^7}) ?
The first derivative of e^{-1/(x^7}) is (7e^{-1/(x^7)})/(x^8)