What is the derivative of log_{e}(ax) ?

The derivative of log_{e}(ax) is 1/x

What is the first derivative of log_{e}(ax) ?

The first derivative of log_{e}(ax) is 1/x

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\frac{d}{d x} (lo g_{e} (a x))

\frac{1}{x}

Solution steps

\frac{d}{d x} (lo g_{e} (a x))

Simplify

lo g_{e} (a x) : ln (a x)

= \frac{d}{d x} (ln (a x))

Apply the chain rule:

\frac{1}{a x} \frac{d}{d x} (a x)

= \frac{1}{a x} \frac{d}{d x} (a x)

\frac{d}{d x} (a x) = a

= \frac{1}{a x} a

Simplify

\frac{1}{a x} a : \frac{1}{x}

= \frac{1}{x}

What is the derivative of log_{e}(ax) ?
The derivative of log_{e}(ax) is 1/x
What is the first derivative of log_{e}(ax) ?
The first derivative of log_{e}(ax) is 1/x