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

The derivative of (-3/(x^4)) is (12)/(x^5)

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

The first derivative of (-3/(x^4)) is (12)/(x^5)

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

\frac{12}{x ^{5}}

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

- 3 (- 4 x^{- 4 - 1}) : \frac{12}{x ^{5}}

= \frac{12}{x ^{5}}

What is the derivative of (-3/(x^4)) ?
The derivative of (-3/(x^4)) is (12)/(x^5)
What is the first derivative of (-3/(x^4)) ?
The first derivative of (-3/(x^4)) is (12)/(x^5)