What is the d/(dt)(5t^{-3}) ?

The d/(dt)(5t^{-3}) is -(15)/(t^4)

What is the first d/(dt)(5t^{-3}) ?

The first d/(dt)(5t^{-3}) is -(15)/(t^4)

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\frac{d}{d t} (5 t^{- 3})

- \frac{15}{t ^{4}}

Solution steps

\frac{d}{d t} (5 t^{- 3})

Take the constant out:

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

= 5 \frac{d}{d t} (t^{- 3})

Apply the Power Rule:

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

= 5 (- 3 t^{- 3 - 1})

Simplify

5 (- 3 t^{- 3 - 1}) : - \frac{15}{t ^{4}}

= - \frac{15}{t ^{4}}