What is (\partial}{\partial u}(\frac{v^2)/u) ?

The answer to (\partial}{\partial u}(\frac{v^2)/u) is -(v^2)/(u^2)

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(\partial}{\partial u}(\frac{v^2)/u)

\frac{\partial}{\partial u} (\frac{v ^{2}}{u})

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

Solution steps

\frac{\partial}{\partial u} (\frac{v ^{2}}{u})

Treat

v

as a constant

Take the constant out:

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

= v^{2} \frac{\partial}{\partial u} (\frac{1}{u})

Apply exponent rule:

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

= v^{2} \frac{\partial}{\partial u} (u^{- 1})

Apply the Power Rule:

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

= v^{2} (- 1 \cdot u^{- 1 - 1})

Simplify

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

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

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What is (\partial}{\partial u}(\frac{v^2)/u) ?
The answer to (\partial}{\partial u}(\frac{v^2)/u) is -(v^2)/(u^2)