What is (\partial)/(\partial x)(5ln((3xy)/(7z))) ?

The answer to (\partial)/(\partial x)(5ln((3xy)/(7z))) is 5/x

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(\partial)/(\partial x)(5ln((3xy)/(7z)))

\frac{\partial}{\partial x} (5 ln (\frac{3 x y}{7 z}))

\frac{5}{x}

Solution steps

\frac{\partial}{\partial x} (5 ln (\frac{3 x y}{7 z}))

Treat

y, z

as constants

Take the constant out:

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

= 5 \frac{\partial}{\partial x} (ln (\frac{3 x y}{7 z}))

Apply the chain rule:

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

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

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

= 5 \cdot \frac{1}{\frac{3 x y}{7 z}} \cdot \frac{3 y}{7 z}

Simplify

5 \cdot \frac{1}{\frac{3 x y}{7 z}} \cdot \frac{3 y}{7 z} : \frac{5}{x}

= \frac{5}{x}

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What is (\partial)/(\partial x)(5ln((3xy)/(7z))) ?
The answer to (\partial)/(\partial x)(5ln((3xy)/(7z))) is 5/x