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

解答

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

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

求解步骤

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

使用连锁律:

\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}})

化简

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

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

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