derivative of ln(1/(2x))

解答

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

- \frac{1}{x}

求解步骤

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

化简

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

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

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用连锁律:

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

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

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

= - \frac{1}{2 x} \cdot 2

化简

- \frac{1}{2 x} \cdot 2 : - \frac{1}{x}

= - \frac{1}{x}

d er i v a t i v e y = 3 e^{x} cos (x)

\int (\frac{x}{7} - \frac{3}{4} x^{4}) d x

2 t^{2} y^{^{''}} + 3 t y^{^{'}} - y = 0

\int_{0}^{\infty} e^{- \frac{x}{2}} d x

x \to 3 lim (\frac{1}{3 - x})