derivative (14)/(ln(x))

解答

导数

\frac{14}{ln ( x )}

- \frac{14}{x ln ^{2} ( x )}

求解步骤

\frac{d}{d x} (\frac{14}{ln ( x )})

将常数提出:

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

= 14 \frac{d}{d x} (\frac{1}{ln ( x )})

使用指数法则:

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

= 14 \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}

= 14 (- \frac{1}{( ln ( x ) ) ^{2}} \cdot \frac{1}{x})

化简

14 (- \frac{1}{ln ^{2} ( x )} \cdot \frac{1}{x}) : - \frac{14}{x ln ^{2} ( x )}

= - \frac{14}{x ln ^{2} ( x )}

\int θ csc^{2} (θ) d θ

[x - y arctan (\frac{y}{x})] d x + x arctan (\frac{y}{x}) d y = 0

x \to \infty lim (\frac{e ^{2 x - 7}}{6 x})

\int \frac{x ^{2} - 7}{7 x} d x

d er i v a t i v e 7 e^{x} x