What is the derivative of a/(x^3) ?

The derivative of a/(x^3) is -(3a)/(x^4)

What is the first derivative of a/(x^3) ?

The first derivative of a/(x^3) is -(3a)/(x^4)

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\frac{d}{d x} (\frac{a}{x ^{3}})

- \frac{3 a}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{a}{x ^{3}})

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

= a (- 3 x^{- 3 - 1})

Simplify

a (- 3 x^{- 3 - 1}) : - \frac{3 a}{x ^{4}}

= - \frac{3 a}{x ^{4}}

What is the derivative of a/(x^3) ?
The derivative of a/(x^3) is -(3a)/(x^4)
What is the first derivative of a/(x^3) ?
The first derivative of a/(x^3) is -(3a)/(x^4)