What is (\partial)/(\partial z)(4ln((3xy)/(7z))) ?

The answer to (\partial)/(\partial z)(4ln((3xy)/(7z))) is -4/z

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(\partial)/(\partial z)(4ln((3xy)/(7z)))

\frac{\partial}{\partial z} (4 ln (\frac{3 x y}{7 z}))

- \frac{4}{z}

Solution steps

\frac{\partial}{\partial z} (4 ln (\frac{3 x y}{7 z}))

Treat

x, y

as constants

Take the constant out:

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

= 4 \frac{\partial}{\partial z} (ln (\frac{3 x y}{7 z}))

Apply the chain rule:

\frac{1}{\frac{3 x y}{7 z}} \frac{\partial}{\partial z} (\frac{3 x y}{7 z})

= \frac{1}{\frac{3 x y}{7 z}} \frac{\partial}{\partial z} (\frac{3 x y}{7 z})

\frac{\partial}{\partial z} (\frac{3 x y}{7 z}) = - \frac{3 x y}{7 z ^{2}}

= 4 \cdot \frac{1}{\frac{3 x y}{7 z}} (- \frac{3 x y}{7 z ^{2}})

Simplify

4 \cdot \frac{1}{\frac{3 x y}{7 z}} (- \frac{3 x y}{7 z ^{2}}) : - \frac{4}{z}

= - \frac{4}{z}

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What is (\partial)/(\partial z)(4ln((3xy)/(7z))) ?
The answer to (\partial)/(\partial z)(4ln((3xy)/(7z))) is -4/z