What is (\partial)/(\partial x)(ln(6xyz)) ?

The answer to (\partial)/(\partial x)(ln(6xyz)) is 1/x

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(\partial)/(\partial x)(ln(6xyz))

\frac{\partial}{\partial x} (ln (6 x yz))

\frac{1}{x}

Solution steps

\frac{\partial}{\partial x} (ln (6 x yz))

Treat

y, z

as constants

Apply the chain rule:

\frac{1}{6 x yz} \frac{\partial}{\partial x} (6 x yz)

= \frac{1}{6 x yz} \frac{\partial}{\partial x} (6 x yz)

\frac{\partial}{\partial x} (6 x yz) = 6 yz

= \frac{1}{6 x yz} \cdot 6 yz

Simplify

\frac{1}{6 x yz} \cdot 6 yz : \frac{1}{x}

= \frac{1}{x}

x \to 8 + lim (\frac{4}{x - 8})

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What is (\partial)/(\partial x)(ln(6xyz)) ?
The answer to (\partial)/(\partial x)(ln(6xyz)) is 1/x