derivative f(x)=x-2ln(1-1/x)

解答

导数

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

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

求解步骤

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

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d x}{d x} = 1

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

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

l a pl a ce t r an s f or m 27 t^{2} sin (6 t - 6 0^{\circ})

\frac{d}{d x} (x^{2} + y^{2} - 5)

\frac{d}{d x} (3 x - \frac{1}{x})

\int_{2}^{6} \frac{x}{x ^{2} + 4 x + 13} d x

d er i v a t i v e f (x) = (2 + 3 x) (6 - 5 x)