What is the derivative of ln(ax+b) ?

The derivative of ln(ax+b) is a/(ax+b)

What is the first derivative of ln(ax+b) ?

The first derivative of ln(ax+b) is a/(ax+b)

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

\frac{a}{a x + b}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{a x + b} a

Simplify

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

= \frac{a}{a x + b}

What is the derivative of ln(ax+b) ?
The derivative of ln(ax+b) is a/(ax+b)
What is the first derivative of ln(ax+b) ?
The first derivative of ln(ax+b) is a/(ax+b)