What is the derivative of 6/(x^{-3}) ?

The derivative of 6/(x^{-3}) is 18x^2

What is the first derivative of 6/(x^{-3}) ?

The first derivative of 6/(x^{-3}) is 18x^2

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\frac{d}{d x} (\frac{6}{x ^{- 3}})

18 x^{2}

Solution steps

\frac{d}{d x} (\frac{6}{x ^{- 3}})

Take the constant out:

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

= 6 \frac{d}{d x} (\frac{1}{x ^{- 3}})

Apply exponent rule:

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

= 6 \frac{d}{d x} (x^{3})

Apply the Power Rule:

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

= 6 \cdot 3 x^{3 - 1}

Simplify

= 18 x^{2}

What is the derivative of 6/(x^{-3}) ?
The derivative of 6/(x^{-3}) is 18x^2
What is the first derivative of 6/(x^{-3}) ?
The first derivative of 6/(x^{-3}) is 18x^2