What is the derivative of ln(1+5/x) ?

The derivative of ln(1+5/x) is -5/(x(x+5))

What is the first derivative of ln(1+5/x) ?

The first derivative of ln(1+5/x) is -5/(x(x+5))

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\frac{d}{d x} (ln (1 + \frac{5}{x}))

- \frac{5}{x ( x + 5 )}

Solution steps

\frac{d}{d x} (ln (1 + \frac{5}{x}))

Apply the chain rule:

\frac{1}{1 + \frac{5}{x}} \frac{d}{d x} (1 + \frac{5}{x})

= \frac{1}{1 + \frac{5}{x}} \frac{d}{d x} (1 + \frac{5}{x})

\frac{d}{d x} (1 + \frac{5}{x}) = - \frac{5}{x ^{2}}

= \frac{1}{1 + \frac{5}{x}} (- \frac{5}{x ^{2}})

Simplify

\frac{1}{1 + \frac{5}{x}} (- \frac{5}{x ^{2}}) : - \frac{5}{x ( x + 5 )}

= - \frac{5}{x ( x + 5 )}

What is the derivative of ln(1+5/x) ?
The derivative of ln(1+5/x) is -5/(x(x+5))
What is the first derivative of ln(1+5/x) ?
The first derivative of ln(1+5/x) is -5/(x(x+5))