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Popular >

derivative of \sqrt[3]{-e^{-x}}

Solution

Solution

\frac{e ^{- x}}{3 ( - e ^{- x} ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

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

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

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

= \frac{1}{3 ( - e ^{- x} ) ^{\frac{2}{3}}} e^{- x}

Simplify

\frac{1}{3 ( - e ^{- x} ) ^{\frac{2}{3}}} e^{- x} : \frac{e ^{- x}}{3 ( - e ^{- x} ) ^{\frac{2}{3}}}

= \frac{e ^{- x}}{3 ( - e ^{- x} ) ^{\frac{2}{3}}}

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\int \frac{x ^{2}}{8} d x

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y = \frac{5}{x}, (\frac{1}{2}, 10)

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\int x^{2} sin (θ) d x

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\int \frac{7 x ^{2}}{( 225 + x ^{2} ) ^{2}} d x

limit as x approaches 0+of (5x^2)(ln(x))

x \to 0 + lim ((5 x^{2}) (ln (x)))

Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[3]{-e^{-x}} ?
The derivative of \sqrt[3]{-e^{-x}} is (e^{-x})/(3(-e^{-x))^{2/3}}
What is the first derivative of \sqrt[3]{-e^{-x}} ?
The first derivative of \sqrt[3]{-e^{-x}} is (e^{-x})/(3(-e^{-x))^{2/3}}