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

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

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

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

\frac{x}{y + z}

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial z} (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}

{\frac{1}{( s ^{2} + 1 ) ( s ^{2} + 4 )}}

x \to 0 lim (\frac{sin ( 4 x )}{2})

\int x^{2} - 10 d x

x \to 0 - lim (\frac{( 4 - x ) - 0}{4})

\frac{d}{d x} (2 e^{2 x} x)

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