derivative of ln((xln(x-1)/(xln(x)+1)))

解答

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

\frac{2 ln ( x ) + 2}{( x ln ( x ) - 1 ) ( x ln ( x ) + 1 )}

求解步骤

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

使用连锁律:

\frac{1}{\frac{x l n ( x ) - 1}{x l n ( x ) + 1}} \frac{d}{d x} (\frac{x ln ( x ) - 1}{x ln ( x ) + 1})

= \frac{1}{\frac{x l n ( x ) - 1}{x l n ( x ) + 1}} \frac{d}{d x} (\frac{x ln ( x ) - 1}{x ln ( x ) + 1})

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

= \frac{1}{\frac{x l n ( x ) - 1}{x l n ( x ) + 1}} \cdot \frac{2 ln ( x ) + 2}{( x ln ( x ) + 1 ) ^{2}}

化简

\frac{1}{\frac{x l n ( x ) - 1}{x l n ( x ) + 1}} \cdot \frac{2 ln ( x ) + 2}{( x ln ( x ) + 1 ) ^{2}} : \frac{2 ln ( x ) + 2}{( x ln ( x ) - 1 ) ( x ln ( x ) + 1 )}

= \frac{2 ln ( x ) + 2}{( x ln ( x ) - 1 ) ( x ln ( x ) + 1 )}

f (x) = \frac{( x + 1 )}{( x - 1 )}

\frac{3 t - 1}{t - 2}

\frac{\partial}{\partial x} (\frac{x}{2 y})

\int \frac{2}{cos ( x )} e^{2 l n (c o s (x))} d x

\int_{1}^{x} \frac{2}{x ^{3}} d x