What is the derivative of ln(sqrt((x+7)/(x-7))) ?

The derivative of ln(sqrt((x+7)/(x-7))) is -7/((x-7)(x+7))

What is the first derivative of ln(sqrt((x+7)/(x-7))) ?

The first derivative of ln(sqrt((x+7)/(x-7))) is -7/((x-7)(x+7))

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derivative of

ln (\frac{x + 7}{x - 7})

- \frac{7}{( x - 7 ) ( x + 7 )}

Solution steps

\frac{d}{d x} (ln (\frac{x + 7}{x - 7}))

Apply the chain rule:

\frac{1}{\frac{x + 7}{x - 7}} \frac{d}{d x} (\frac{x + 7}{x - 7})

= \frac{1}{\frac{x + 7}{x - 7}} \frac{d}{d x} (\frac{x + 7}{x - 7})

\frac{d}{d x} (\frac{x + 7}{x - 7}) = - \frac{7}{x + 7 ( x - 7 ) ^{\frac{3}{2}}}

= \frac{1}{\frac{x + 7}{x - 7}} (- \frac{7}{x + 7 ( x - 7 ) ^{\frac{3}{2}}})

Simplify

\frac{1}{\frac{x + 7}{x - 7}} (- \frac{7}{x + 7 ( x - 7 ) ^{\frac{3}{2}}}) : - \frac{7}{( x - 7 ) ( x + 7 )}

= - \frac{7}{( x - 7 ) ( x + 7 )}

What is the derivative of ln(sqrt((x+7)/(x-7))) ?
The derivative of ln(sqrt((x+7)/(x-7))) is -7/((x-7)(x+7))
What is the first derivative of ln(sqrt((x+7)/(x-7))) ?
The first derivative of ln(sqrt((x+7)/(x-7))) is -7/((x-7)(x+7))