What is the derivative of ln(sqrt((x+8/(x-8)))) ?

The derivative of ln(sqrt((x+8/(x-8)))) is -8/((x-8)(x+8))

What is the first derivative of ln(sqrt((x+8/(x-8)))) ?

The first derivative of ln(sqrt((x+8/(x-8)))) is -8/((x-8)(x+8))

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\frac{d}{d x} (ln (\frac{x + 8}{x - 8}))

- \frac{8}{( x - 8 ) ( x + 8 )}

Solution steps

\frac{d}{d x} (ln (\frac{x + 8}{x - 8}))

Apply the chain rule:

\frac{1}{\frac{x + 8}{x - 8}} \frac{d}{d x} (\frac{x + 8}{x - 8})

= \frac{1}{\frac{x + 8}{x - 8}} \frac{d}{d x} (\frac{x + 8}{x - 8})

\frac{d}{d x} (\frac{x + 8}{x - 8}) = - \frac{8}{x + 8 ( x - 8 ) ^{\frac{3}{2}}}

= \frac{1}{\frac{x + 8}{x - 8}} (- \frac{8}{x + 8 ( x - 8 ) ^{\frac{3}{2}}})

Simplify

\frac{1}{\frac{x + 8}{x - 8}} (- \frac{8}{x + 8 ( x - 8 ) ^{\frac{3}{2}}}) : - \frac{8}{( x - 8 ) ( x + 8 )}

= - \frac{8}{( x - 8 ) ( x + 8 )}

\int \frac{2 x ^{2} + 4 x - 3}{x ^{2}} d x

y^{^{''}} + 121 y = cos (10 t)

\int 2^{\frac{1}{2}}

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

x \to + 0 lim (\frac{x ^{3}}{ln ∣ x ∣})

What is the derivative of ln(sqrt((x+8/(x-8)))) ?
The derivative of ln(sqrt((x+8/(x-8)))) is -8/((x-8)(x+8))
What is the first derivative of ln(sqrt((x+8/(x-8)))) ?
The first derivative of ln(sqrt((x+8/(x-8)))) is -8/((x-8)(x+8))