What is (\partial)/(\partial y)(ln(xyz)) ?

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

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(\partial)/(\partial y)(ln(xyz))

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

\frac{1}{y}

Solution steps

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

Treat

x, z

as constants

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (x yz) = x z

= \frac{1}{x yz} x z

Simplify

\frac{1}{x yz} x z : \frac{1}{y}

= \frac{1}{y}

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