derivative of ln((2-x/(2+x)))

解答

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

- \frac{4}{( - x + 2 ) ( x + 2 )}

求解步骤

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

使用连锁律:

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

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

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

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

化简

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

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

\int \frac{arctan ^{4} ( x )}{1 + x ^{2}} d x

x \to 0 lim (ln ((\frac{1}{x})^{x}))

\int (\frac{ln ( x )}{x ^{3}}) d x

\frac{d}{d x} (\frac{10}{( x - 2 ) ^{3}})

\frac{\partial}{\partial y} (4 x^{2} + 6 x y + y^{2})