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

解答

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

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

求解步骤

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

使用连锁律:

\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}})

化简

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

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

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

d er i v a t i v e f (x) = x (x - 6)^{2}

d er i v a t i v e 5 e^{x} + \frac{4}{3 x}

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

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