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

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

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

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

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derivative of

ln (\frac{q}{7})

\frac{1}{q}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{q}

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