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

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

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(\partial)/(\partial z)(ln(xyz))

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

\frac{1}{z}

Solution steps

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

Treat

x, y

as constants

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{z}

\frac{d}{d x} (x^{2} + a^{2})

3 x + 8

\int e^{c o s (37 t)} sin (37 t) d t

x \to - 9 lim (\frac{x + 8}{x + 9})

\frac{\partial}{\partial x} (7 y^{9} + 5 y^{7} x^{4})

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