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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\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}

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