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Popular >

derivative of e^{-1/(x^3})

Solution

\frac{d}{d x} (e^{- \frac{1}{x ^{3}}})

Solution

\frac{3 e ^{- \frac{1}{x ^{3}}}}{x ^{4}}

Solution steps

\frac{d}{d x} (e^{- \frac{1}{x ^{3}}})

Apply the chain rule:

e^{- \frac{1}{x ^{3}}} \frac{d}{d x} (- \frac{1}{x ^{3}})

= e^{- \frac{1}{x ^{3}}} \frac{d}{d x} (- \frac{1}{x ^{3}})

\frac{d}{d x} (- \frac{1}{x ^{3}}) = \frac{3}{x ^{4}}

= e^{- \frac{1}{x ^{3}}} \frac{3}{x ^{4}}

Multiply fractions:

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

= \frac{3 e ^{- \frac{1}{x ^{3}}}}{x ^{4}}

Popular Examples

integral of 6x^5e^{7x^6}

\int 6 x^{5} e^{7 x^{6}} d x

derivative of x^{2/3}(6-x^{1/3})

\frac{d}{d x} (x^{\frac{2}{3}} (6 - x)^{\frac{1}{3}})

integral from 8 to 13 of y/(y^2-4y-5)

\int_{8}^{13} \frac{y}{y ^{2} - 4 y - 5} d y

y^{''}-3y^'+2y=4e^{2t}

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 e^{2 t}

derivative of sqrt(-3x+7)

\frac{d}{d x} (- 3 x + 7)

Frequently Asked Questions (FAQ)

What is the derivative of e^{-1/(x^3}) ?
The derivative of e^{-1/(x^3}) is (3e^{-1/(x^3)})/(x^4)
What is the first derivative of e^{-1/(x^3}) ?
The first derivative of e^{-1/(x^3}) is (3e^{-1/(x^3)})/(x^4)