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

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

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

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

\frac{7}{x}

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

= 7 \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}

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

Simplify

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

= \frac{7}{x}

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