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Popular >

derivative of ln(1+a/x)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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