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Popular >

derivative of ln((x+6/(x-6)))

Solution

\frac{d}{d x} (ln (\frac{x + 6}{x - 6}))

Solution

- \frac{12}{( x + 6 ) ( x - 6 )}

Solution steps

\frac{d}{d x} (ln (\frac{x + 6}{x - 6}))

Apply the chain rule:

\frac{1}{\frac{x + 6}{x - 6}} \frac{d}{d x} (\frac{x + 6}{x - 6})

= \frac{1}{\frac{x + 6}{x - 6}} \frac{d}{d x} (\frac{x + 6}{x - 6})

\frac{d}{d x} (\frac{x + 6}{x - 6}) = - \frac{12}{( x - 6 ) ^{2}}

= \frac{1}{\frac{x + 6}{x - 6}} (- \frac{12}{( x - 6 ) ^{2}})

Simplify

\frac{1}{\frac{x + 6}{x - 6}} (- \frac{12}{( x - 6 ) ^{2}}) : - \frac{12}{( x + 6 ) ( x - 6 )}

= - \frac{12}{( x + 6 ) ( x - 6 )}

Popular Examples

integral of (tan^2(7x))/(csc(7x))

\int \frac{tan ^{2} ( 7 x )}{csc ( 7 x )} d x

derivative of f(x)=sqrt(x)(x-6)^2 derivative of

f (x) = x (x - 6)^{2}

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

(\partial)/(\partial x)(-1/(2x)+1/(2x^2))

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

Frequently Asked Questions (FAQ)

What is the derivative of ln((x+6/(x-6))) ?
The derivative of ln((x+6/(x-6))) is -(12)/((x+6)(x-6))
What is the first derivative of ln((x+6/(x-6))) ?
The first derivative of ln((x+6/(x-6))) is -(12)/((x+6)(x-6))