What is the first d/(dv)(m/v) ?

The first d/(dv)(m/v) is -m/(v^2)

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d/(dv)(m/v)

\frac{d}{d v} (\frac{m}{v})

- \frac{m}{v ^{2}}

Solution steps

\frac{d}{d v} (\frac{m}{v})

Take the constant out:

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

= m \frac{d}{d v} (\frac{1}{v})

Apply exponent rule:

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

= m \frac{d}{d v} (v^{- 1})

Apply the Power Rule:

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

= m (- 1 \cdot v^{- 1 - 1})

Simplify

m (- 1 \cdot v^{- 1 - 1}) : - \frac{m}{v ^{2}}

= - \frac{m}{v ^{2}}

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