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

The derivative of ln((x+3)/(sqrt(x-1))) is (x-5)/(2(x+3)(x-1))

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

The first derivative of ln((x+3)/(sqrt(x-1))) is (x-5)/(2(x+3)(x-1))

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derivative of

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

\frac{x - 5}{2 ( 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{x - 5}{2 ( x - 1 ) x - 1}

= \frac{1}{\frac{x + 3}{x - 1}} \cdot \frac{x - 5}{2 ( x - 1 ) x - 1}

Simplify

\frac{1}{\frac{x + 3}{x - 1}} \cdot \frac{x - 5}{2 ( x - 1 ) x - 1} : \frac{x - 5}{2 ( x + 3 ) ( x - 1 )}

= \frac{x - 5}{2 ( x + 3 ) ( x - 1 )}

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What is the derivative of ln((x+3)/(sqrt(x-1))) ?
The derivative of ln((x+3)/(sqrt(x-1))) is (x-5)/(2(x+3)(x-1))
What is the first derivative of ln((x+3)/(sqrt(x-1))) ?
The first derivative of ln((x+3)/(sqrt(x-1))) is (x-5)/(2(x+3)(x-1))