What is the derivative of ln(x/7) ?

The derivative of ln(x/7) is 1/x

What is the first derivative of ln(x/7) ?

The first derivative of ln(x/7) is 1/x

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\frac{d}{d x} (ln (\frac{x}{7}))

\frac{1}{x}

Solution steps

\frac{d}{d x} (ln (\frac{x}{7}))

Apply the chain rule:

\frac{1}{\frac{x}{7}} \frac{d}{d x} (\frac{x}{7})

= \frac{1}{\frac{x}{7}} \frac{d}{d x} (\frac{x}{7})

\frac{d}{d x} (\frac{x}{7}) = \frac{1}{7}

= \frac{1}{\frac{x}{7}} \cdot \frac{1}{7}

Simplify

\frac{1}{\frac{x}{7}} \cdot \frac{1}{7} : \frac{1}{x}

= \frac{1}{x}

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What is the derivative of ln(x/7) ?
The derivative of ln(x/7) is 1/x
What is the first derivative of ln(x/7) ?
The first derivative of ln(x/7) is 1/x