derivative of (13/(ln(x)))

解答

\frac{d}{d x} (\frac{13}{ln ( x )})

- \frac{13}{x ln ^{2} ( x )}

求解步骤

\frac{d}{d x} (\frac{13}{ln ( x )})

将常数提出:

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

= 13 \frac{d}{d x} (\frac{1}{ln ( x )})

使用指数法则:

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

= 13 \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}

= 13 (- \frac{1}{( ln ( x ) ) ^{2}} \cdot \frac{1}{x})

化简

13 (- \frac{1}{ln ^{2} ( x )} \cdot \frac{1}{x}) : - \frac{13}{x ln ^{2} ( x )}

= - \frac{13}{x ln ^{2} ( x )}

x \to \infty lim (\frac{e ^{2 x} + e ^{x}}{e ^{2 x} - 1} 1)

in v erse l a pl a ce \frac{1}{( s + 2 ) ( s - 1 ) ^{5}}

x \to \infty lim (2 - x^{2})

\int 5 x^{2} + 1 d x

\int_{0}^{3} x x^{2} + 16 d x