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

The derivative of ln((6-x)/(6+x)) is -(12)/((-x+6)(x+6))

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 2 - y^{2} d y

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

\int \frac{e ^{x}}{( e ^{x} - 3 ) ( e ^{2 x} + 1 )} d x

\frac{d}{d x} (e^{x^{2} - y})

\int 2 x (x^{2} + 5)^{- 4} d x

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