What is the d/(ds)(2/(s^3)) ?

The d/(ds)(2/(s^3)) is -6/(s^4)

What is the first d/(ds)(2/(s^3)) ?

The first d/(ds)(2/(s^3)) is -6/(s^4)

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\frac{d}{d s} (\frac{2}{s ^{3}})

- \frac{6}{s ^{4}}

Solution steps

\frac{d}{d s} (\frac{2}{s ^{3}})

Take the constant out:

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

= 2 \frac{d}{d s} (\frac{1}{s ^{3}})

Apply exponent rule:

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

= 2 \frac{d}{d s} (s^{- 3})

Apply the Power Rule:

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

= 2 (- 3 s^{- 3 - 1})

Simplify

2 (- 3 s^{- 3 - 1}) : - \frac{6}{s ^{4}}

= - \frac{6}{s ^{4}}