What is the first d/(dt)(k/t) ?

The first d/(dt)(k/t) is -k/(t^2)

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d/(dt)(k/t)

\frac{d}{d t} (\frac{k}{t})

- \frac{k}{t ^{2}}

Solution steps

\frac{d}{d t} (\frac{k}{t})

Take the constant out:

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

= k \frac{d}{d t} (\frac{1}{t})

Apply exponent rule:

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

= k \frac{d}{d t} (t^{- 1})

Apply the Power Rule:

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

= k (- 1 \cdot t^{- 1 - 1})

Simplify

k (- 1 \cdot t^{- 1 - 1}) : - \frac{k}{t ^{2}}

= - \frac{k}{t ^{2}}

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