What is the derivative of ln(ax) ?

The derivative of ln(ax) is 1/x

What is the first derivative of ln(ax) ?

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

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

\frac{1}{x}

Solution steps

\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}

\int \frac{3}{y ^{π}} d y

\frac{\partial}{\partial x} (\frac{8.31 y}{x})

\frac{\partial}{\partial x} (x cos (y) - 2 y)

\int (x^{2} \frac{e ^{- 2 x}}{2}) d x

7 (t + 1) \frac{d y}{d t} - 6 y = 6 t