What is the derivative of-(81/(x^4)) ?

The derivative of-(81/(x^4)) is (324)/(x^5)

What is the first derivative of-(81/(x^4)) ?

The first derivative of-(81/(x^4)) is (324)/(x^5)

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\frac{d}{d x} (- \frac{81}{x ^{4}})

\frac{324}{x ^{5}}

Solution steps

\frac{d}{d x} (- \frac{81}{x ^{4}})

Take the constant out:

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

= - 81 \frac{d}{d x} (\frac{1}{x ^{4}})

Apply exponent rule:

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

= - 81 \frac{d}{d x} (x^{- 4})

Apply the Power Rule:

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

= - 81 (- 4 x^{- 4 - 1})

Simplify

- 81 (- 4 x^{- 4 - 1}) : \frac{324}{x ^{5}}

= \frac{324}{x ^{5}}

What is the derivative of-(81/(x^4)) ?
The derivative of-(81/(x^4)) is (324)/(x^5)
What is the first derivative of-(81/(x^4)) ?
The first derivative of-(81/(x^4)) is (324)/(x^5)