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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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