What is the derivative of ln((x-2/(x+1))) ?

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

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

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

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\frac{d}{d x} (ln (\frac{x - 2}{x + 1}))

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

Solution steps

\frac{d}{d x} (ln (\frac{x - 2}{x + 1}))

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int (2 - x)^{2} ln (4 x) d x

\frac{11}{3} t^{3} + 11 t^{2}

\frac{d}{d x} ((6 x^{2} + 6) e^{- x})

\frac{d}{d x} (e^{l n (2)})

y = 3 x^{3} - 3 x, (- 1, 0)

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