What is (\partial)/(\partial v)(1/v) ?

The answer to (\partial)/(\partial v)(1/v) is -1/(v^2)

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(\partial)/(\partial v)(1/v)

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

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

Solution steps

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

Apply exponent rule:

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

= \frac{\partial}{\partial 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}}

\frac{d}{d x} (3 x^{2} - 12 x + 5)

y \cdot d x + x^{2} \cdot d y = 0

\int \frac{2}{x} d x

\frac{d y}{d x} + y cos (x) = 2 cos (x)

\frac{\partial}{\partial x} (y e^{y x})

What is (\partial)/(\partial v)(1/v) ?
The answer to (\partial)/(\partial v)(1/v) is -1/(v^2)