What is the derivative of ln(x/a) ?

The derivative of ln(x/a) is 1/x

What is the first derivative of ln(x/a) ?

The first derivative of ln(x/a) is 1/x

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

\frac{1}{x}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{\frac{x}{a}} \cdot \frac{1}{a}

Simplify

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

= \frac{1}{x}

What is the derivative of ln(x/a) ?
The derivative of ln(x/a) is 1/x
What is the first derivative of ln(x/a) ?
The first derivative of ln(x/a) is 1/x