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

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

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

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

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

\frac{1}{x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{x}

\int_{- a}^{a} \frac{1}{( s - x ) ^{2}} d x

\frac{d}{d x} (\frac{x ^{2} - 4}{x ^{2} - 2 x})

\int \frac{2}{x ^{\frac{2}{3}}} d x

2 y \cdot \frac{d y}{d x} = x (y^{2} + 1)

\frac{d}{d x} (in (x^{2} - 5))

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