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Popular >

derivative of ln((x+a/(x-a)))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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