derivative of ln(2x-sqrt(x))

解答

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

\frac{4 x - 1}{2 x ( 2 x - x )}

求解步骤

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

使用连锁律:

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

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

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

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

化简

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

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

(x + y) \cdot y^{^{'}} = 2 \cdot x + 2 \cdot y - 3

\int \frac{e ^{x - 1}}{x} d x

d er i v a t i v e 35 x - x x

x \to 0 lim (sin (4 x))

\int \frac{x - 1}{x ^{2} - 4 x - 5} d x