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

The derivative of (e^{-1})/(x^4) is -4/(ex^5)

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

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

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derivative of

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= e^{- 1} (- 4 x^{- 4 - 1})

Simplify

e^{- 1} (- 4 x^{- 4 - 1}) : - \frac{4}{e x ^{5}}

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

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