What is (\partial)/(\partial y)(xln(yz)) ?

The answer to (\partial)/(\partial y)(xln(yz)) is x/y

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(\partial)/(\partial y)(xln(yz))

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

\frac{x}{y}

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= x \frac{1}{yz} z

Simplify

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

= \frac{x}{y}

What is (\partial)/(\partial y)(xln(yz)) ?
The answer to (\partial)/(\partial y)(xln(yz)) is x/y