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

The derivative of (-4)/(x^3) is (12)/(x^4)

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

The first derivative of (-4)/(x^3) is (12)/(x^4)

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derivative of

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

\frac{12}{x ^{4}}

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

= - 4 (- 3 x^{- 3 - 1})

Simplify

- 4 (- 3 x^{- 3 - 1}) : \frac{12}{x ^{4}}

= \frac{12}{x ^{4}}

What is the derivative of (-4)/(x^3) ?
The derivative of (-4)/(x^3) is (12)/(x^4)
What is the first derivative of (-4)/(x^3) ?
The first derivative of (-4)/(x^3) is (12)/(x^4)