What is the d/(d{x)}(ln({x}{y}{z})) ?

The d/(d{x)}(ln({x}{y}{z})) is 1/({x)}

What is the first d/(d{x)}(ln({x}{y}{z})) ?

The first d/(d{x)}(ln({x}{y}{z})) is 1/({x)}

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\frac{d}{d x} (ln (x y z))

\frac{1}{x}

Solution steps

\frac{d}{d x} (ln (x y z))

Apply the chain rule:

\frac{1}{x y z} \frac{d}{d x} (x y z)

= \frac{1}{x y z} \frac{d}{d x} (x y z)

\frac{d}{d x} (x y z) = y z

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

Simplify

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

= \frac{1}{x}

What is the d/(d{x)}(ln({x}{y}{z})) ?
The d/(d{x)}(ln({x}{y}{z})) is 1/({x)}
What is the first d/(d{x)}(ln({x}{y}{z})) ?
The first d/(d{x)}(ln({x}{y}{z})) is 1/({x)}