What is the derivative of ln(3/x) ?

The derivative of ln(3/x) is -1/x

What is the first derivative of ln(3/x) ?

The first derivative of ln(3/x) is -1/x

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\frac{d}{d x} (ln (\frac{3}{x}))

- \frac{1}{x}

Solution steps

\frac{d}{d x} (ln (\frac{3}{x}))

Apply the chain rule:

\frac{1}{\frac{3}{x}} \frac{d}{d x} (\frac{3}{x})

= \frac{1}{\frac{3}{x}} \frac{d}{d x} (\frac{3}{x})

\frac{d}{d x} (\frac{3}{x}) = - \frac{3}{x ^{2}}

= \frac{1}{\frac{3}{x}} (- \frac{3}{x ^{2}})

Simplify

\frac{1}{\frac{3}{x}} (- \frac{3}{x ^{2}}) : - \frac{1}{x}

= - \frac{1}{x}

x \to 2 + lim (\frac{1}{( x - 2 ) ^{3}})

x \to 0 lim (\frac{x}{x ^{2} - 4 x})

\int \frac{1}{( a x + b ) ^{2}} d x

x \to 3 lim (\frac{1}{∣ x - 3 ∣})

\frac{d}{d x} (x^{2} \cdot 2 x)

What is the derivative of ln(3/x) ?
The derivative of ln(3/x) is -1/x
What is the first derivative of ln(3/x) ?
The first derivative of ln(3/x) is -1/x