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

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

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

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

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derivative of

y = 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}

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