What is (\partial)/(\partial x)(8ln((3xy)/(5z))) ?

The answer to (\partial)/(\partial x)(8ln((3xy)/(5z))) is 8/x

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(\partial)/(\partial x)(8ln((3xy)/(5z)))

\frac{\partial}{\partial x} (8 ln (\frac{3 x y}{5 z}))

\frac{8}{x}

Solution steps

\frac{\partial}{\partial x} (8 ln (\frac{3 x y}{5 z}))

Treat

y, z

as constants

Take the constant out:

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

= 8 \frac{\partial}{\partial x} (ln (\frac{3 x y}{5 z}))

Apply the chain rule:

\frac{1}{\frac{3 x y}{5 z}} \frac{\partial}{\partial x} (\frac{3 x y}{5 z})

= \frac{1}{\frac{3 x y}{5 z}} \frac{\partial}{\partial x} (\frac{3 x y}{5 z})

\frac{\partial}{\partial x} (\frac{3 x y}{5 z}) = \frac{3 y}{5 z}

= 8 \cdot \frac{1}{\frac{3 x y}{5 z}} \cdot \frac{3 y}{5 z}

Simplify

8 \cdot \frac{1}{\frac{3 x y}{5 z}} \cdot \frac{3 y}{5 z} : \frac{8}{x}

= \frac{8}{x}

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What is (\partial)/(\partial x)(8ln((3xy)/(5z))) ?
The answer to (\partial)/(\partial x)(8ln((3xy)/(5z))) is 8/x