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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (\frac{m}{x ^{a} y ^{b} z ^{c}})

\frac{\partial}{\partial x} (\frac{3}{8} x y)

\int t^{2} e^{- (s - 1) t} d t

\frac{d}{d x} (a cos (b x + c) + d)

6 x^{2} - 2 x, x^{3} - 6 x + 3

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