What is the first d/(dv)(1/v) ?

The first d/(dv)(1/v) is -1/(v^2)

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d/(dv)(1/v)

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

- \frac{1}{v ^{2}}

Solution steps

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

= - 1 \cdot v^{- 1 - 1}

Simplify

- 1 \cdot v^{- 1 - 1} : - \frac{1}{v ^{2}}

= - \frac{1}{v ^{2}}

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