What is (\partial)/(\partial x)(ln((2xy)/(5z))) ?

The answer to (\partial)/(\partial x)(ln((2xy)/(5z))) is 1/x

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(\partial)/(\partial x)(ln((2xy)/(5z)))

\frac{\partial}{\partial x} (ln (\frac{2 x y}{5 z}))

\frac{1}{x}

Solution steps

\frac{\partial}{\partial x} (ln (\frac{2 x y}{5 z}))

Treat

y, z

as constants

Apply the chain rule:

\frac{1}{\frac{2 x y}{5 z}} \frac{\partial}{\partial x} (\frac{2 x y}{5 z})

= \frac{1}{\frac{2 x y}{5 z}} \frac{\partial}{\partial x} (\frac{2 x y}{5 z})

\frac{\partial}{\partial x} (\frac{2 x y}{5 z}) = \frac{2 y}{5 z}

= \frac{1}{\frac{2 x y}{5 z}} \cdot \frac{2 y}{5 z}

Simplify

\frac{1}{\frac{2 x y}{5 z}} \cdot \frac{2 y}{5 z} : \frac{1}{x}

= \frac{1}{x}

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What is (\partial)/(\partial x)(ln((2xy)/(5z))) ?
The answer to (\partial)/(\partial x)(ln((2xy)/(5z))) is 1/x