What is the derivative of ln(1+2/x) ?

The derivative of ln(1+2/x) is -2/(x(x+2))

What is the first derivative of ln(1+2/x) ?

The first derivative of ln(1+2/x) is -2/(x(x+2))

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\frac{d}{d x} (ln (1 + \frac{2}{x}))

- \frac{2}{x ( x + 2 )}

Solution steps

\frac{d}{d x} (ln (1 + \frac{2}{x}))

Apply the chain rule:

\frac{1}{1 + \frac{2}{x}} \frac{d}{d x} (1 + \frac{2}{x})

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

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

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

Simplify

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

= - \frac{2}{x ( x + 2 )}

What is the derivative of ln(1+2/x) ?
The derivative of ln(1+2/x) is -2/(x(x+2))
What is the first derivative of ln(1+2/x) ?
The first derivative of ln(1+2/x) is -2/(x(x+2))