What is the derivative of ln((x+3)/(x-1)) ?

The derivative of ln((x+3)/(x-1)) is -4/((x+3)(x-1))

What is the first derivative of ln((x+3)/(x-1)) ?

The first derivative of ln((x+3)/(x-1)) is -4/((x+3)(x-1))

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derivative of

ln (\frac{x + 3}{x - 1})

- \frac{4}{( x + 3 ) ( x - 1 )}

Solution steps

\frac{d}{d x} (ln (\frac{x + 3}{x - 1}))

Apply the chain rule:

\frac{1}{\frac{x + 3}{x - 1}} \frac{d}{d x} (\frac{x + 3}{x - 1})

= \frac{1}{\frac{x + 3}{x - 1}} \frac{d}{d x} (\frac{x + 3}{x - 1})

\frac{d}{d x} (\frac{x + 3}{x - 1}) = - \frac{4}{( x - 1 ) ^{2}}

= \frac{1}{\frac{x + 3}{x - 1}} (- \frac{4}{( x - 1 ) ^{2}})

Simplify

\frac{1}{\frac{x + 3}{x - 1}} (- \frac{4}{( x - 1 ) ^{2}}) : - \frac{4}{( x + 3 ) ( x - 1 )}

= - \frac{4}{( x + 3 ) ( x - 1 )}

121 y^{^{''}} - 16 y = 0

\frac{\partial}{\partial x} ((x + y)^{2})

n = 1 \sum \infty \frac{1}{n ^{2} + 3 n + 2}

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

\int \frac{6 x ^{3} - 12 x ^{2} + 8}{x ^{2} - 2 x} d x

What is the derivative of ln((x+3)/(x-1)) ?
The derivative of ln((x+3)/(x-1)) is -4/((x+3)(x-1))
What is the first derivative of ln((x+3)/(x-1)) ?
The first derivative of ln((x+3)/(x-1)) is -4/((x+3)(x-1))