derivative 4/(ln(x))

解答

导数

\frac{4}{ln ( x )}

- \frac{4}{x ln ^{2} ( x )}

求解步骤

\frac{d}{d x} (\frac{4}{ln ( x )})

将常数提出:

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

= 4 \frac{d}{d x} (\frac{1}{ln ( x )})

使用指数法则:

\frac{1}{a} = a^{- 1}

= 4 \frac{d}{d x} (ln^{- 1} (x))

使用连锁律:

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

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

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

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

化简

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

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

x \to \frac{23}{2} lim (\frac{3}{2})

\int x^{2} ln (7 x) d x

\int \frac{4}{5} - \frac{7}{x} d x

d er i v a t i v e e^{x} (x^{2} + 1)

\frac{d}{d x} (\frac{e ^{x}}{1 - e ^{- x}})