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Popular Calculus >

derivative of e^{-1/(x^4})

Solution

\frac{d}{d x} (e^{- \frac{1}{x ^{4}}})

Solution

\frac{4 e ^{- \frac{1}{x ^{4}}}}{x ^{5}}

Solution steps

\frac{d}{d x} (e^{- \frac{1}{x ^{4}}})

Apply the chain rule:

e^{- \frac{1}{x ^{4}}} \frac{d}{d x} (- \frac{1}{x ^{4}})

= e^{- \frac{1}{x ^{4}}} \frac{d}{d x} (- \frac{1}{x ^{4}})

\frac{d}{d x} (- \frac{1}{x ^{4}}) = \frac{4}{x ^{5}}

= e^{- \frac{1}{x ^{4}}} \frac{4}{x ^{5}}

Multiply fractions:

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

= \frac{4 e ^{- \frac{1}{x ^{4}}}}{x ^{5}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of e^{-1/(x^4}) ?
The derivative of e^{-1/(x^4}) is (4e^{-1/(x^4)})/(x^5)
What is the first derivative of e^{-1/(x^4}) ?
The first derivative of e^{-1/(x^4}) is (4e^{-1/(x^4)})/(x^5)