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Popular >

derivative of ln((4-x/(4+x)))

Solution

\frac{d}{d x} (ln (\frac{4 - x}{4 + x}))

Solution

- \frac{8}{( - x + 4 ) ( x + 4 )}

Solution steps

\frac{d}{d x} (ln (\frac{4 - x}{4 + x}))

Apply the chain rule:

\frac{1}{\frac{4 - x}{4 + x}} \frac{d}{d x} (\frac{4 - x}{4 + x})

= \frac{1}{\frac{4 - x}{4 + x}} \frac{d}{d x} (\frac{4 - x}{4 + x})

\frac{d}{d x} (\frac{4 - x}{4 + x}) = - \frac{8}{( 4 + x ) ^{2}}

= \frac{1}{\frac{4 - x}{4 + x}} (- \frac{8}{( 4 + x ) ^{2}})

Simplify

\frac{1}{\frac{4 - x}{4 + x}} (- \frac{8}{( 4 + x ) ^{2}}) : - \frac{8}{( - x + 4 ) ( x + 4 )}

= - \frac{8}{( - x + 4 ) ( x + 4 )}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ln((4-x/(4+x))) ?
The derivative of ln((4-x/(4+x))) is -8/((-x+4)(x+4))
What is the first derivative of ln((4-x/(4+x))) ?
The first derivative of ln((4-x/(4+x))) is -8/((-x+4)(x+4))