What is the derivative of ln((x+3/(x-3))) ?

The derivative of ln((x+3/(x-3))) is -6/((x+3)(x-3))

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

The first derivative of ln((x+3/(x-3))) is -6/((x+3)(x-3))

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\frac{d}{d x} (ln (\frac{x + 3}{x - 3}))

- \frac{6}{( x + 3 ) ( x - 3 )}

Solution steps

\frac{d}{d x} (ln (\frac{x + 3}{x - 3}))

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x + 3}{x - 3}) = - \frac{6}{( x - 3 ) ^{2}}

= \frac{1}{\frac{x + 3}{x - 3}} (- \frac{6}{( x - 3 ) ^{2}})

Simplify

\frac{1}{\frac{x + 3}{x - 3}} (- \frac{6}{( x - 3 ) ^{2}}) : - \frac{6}{( x + 3 ) ( x - 3 )}

= - \frac{6}{( x + 3 ) ( x - 3 )}

\int \frac{1}{x 8 - ln ^{2} ( x ) + 2 ln ( x )} d x

x \to 0 + lim (6 x ln (x))

x \to - 2 lim (x^{2} - 4)

\frac{\partial}{\partial x} (2 (y - 5) (x + 5))

\frac{d}{d x} (arcsec (8 x))

What is the derivative of ln((x+3/(x-3))) ?
The derivative of ln((x+3/(x-3))) is -6/((x+3)(x-3))
What is the first derivative of ln((x+3/(x-3))) ?
The first derivative of ln((x+3/(x-3))) is -6/((x+3)(x-3))