What is (\partial)/(\partial y)(xln(y+z)) ?

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

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(\partial)/(\partial y)(xln(y+z))

\frac{\partial}{\partial y} (x ln (y + z))

\frac{x}{y + z}

Solution steps

\frac{\partial}{\partial y} (x ln (y + z))

Treat

x, z

as constants

Take the constant out:

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

= x \frac{\partial}{\partial y} (ln (y + z))

Apply the chain rule:

\frac{1}{y + z} \frac{\partial}{\partial y} (y + z)

= \frac{1}{y + z} \frac{\partial}{\partial y} (y + z)

\frac{\partial}{\partial y} (y + z) = 1

= x \frac{1}{y + z} \cdot 1

Simplify

x \frac{1}{y + z} \cdot 1 : \frac{x}{y + z}

= \frac{x}{y + z}

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