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

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

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(\partial)/(\partial u)(v/u)

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

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

Solution steps

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

Treat

v

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\int_{0}^{3} ∣ 2 x - 4 ∣ d x

\int (7 x^{6} + \frac{x}{7}) d x

\frac{d y}{d x}, x^{2} = y^{3}

\frac{d}{d x} ((arccos (x))^{10})

\frac{d}{d x} ((2 - x)^{4})

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