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Popular >

derivative of ln((x+3/(x-3)))

Solution

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

Solution

- \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 )}

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limit as x approaches 0+of 6sqrt(x)ln(x)

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

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Frequently Asked Questions (FAQ)

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))