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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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