What is the d/(dt)(1/(t^3)) ?

The d/(dt)(1/(t^3)) is -3/(t^4)

What is the first d/(dt)(1/(t^3)) ?

The first d/(dt)(1/(t^3)) is -3/(t^4)

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\frac{d}{d t} (\frac{1}{t ^{3}})

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

Solution steps

\frac{d}{d t} (\frac{1}{t ^{3}})

Apply exponent rule:

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

= \frac{d}{d t} (t^{- 3})

Apply the Power Rule:

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

= - 3 t^{- 3 - 1}

Simplify

- 3 t^{- 3 - 1} : - \frac{3}{t ^{4}}

= - \frac{3}{t ^{4}}

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