What is (\partial)/(\partial u)(v/(6+uvw)) ?

The answer to (\partial)/(\partial u)(v/(6+uvw)) is -(v^2w)/((6+vuw)^2)

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(\partial)/(\partial u)(v/(6+uvw))

\frac{\partial}{\partial u} (\frac{v}{6 + uv w})

- \frac{v ^{2} w}{( 6 + vu w ) ^{2}}

Solution steps

\frac{\partial}{\partial u} (\frac{v}{6 + uv w})

Treat

v, w

as constants

Take the constant out:

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

= v \frac{\partial}{\partial u} (\frac{1}{6 + uv w})

Apply exponent rule:

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

= v \frac{\partial}{\partial u} ((6 + uv w)^{- 1})

Apply the chain rule:

- \frac{1}{( 6 + uv w ) ^{2}} \frac{\partial}{\partial u} (6 + uv w)

= - \frac{1}{( 6 + uv w ) ^{2}} \frac{\partial}{\partial u} (6 + uv w)

\frac{\partial}{\partial u} (6 + uv w) = v w

= v (- \frac{1}{( 6 + uv w ) ^{2}} v w)

Simplify

v (- \frac{1}{( 6 + uv w ) ^{2}} v w) : - \frac{v ^{2} w}{( 6 + vu w ) ^{2}}

= - \frac{v ^{2} w}{( 6 + vu w ) ^{2}}

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What is (\partial)/(\partial u)(v/(6+uvw)) ?
The answer to (\partial)/(\partial u)(v/(6+uvw)) is -(v^2w)/((6+vuw)^2)