derivative of (2x/(ln(x)))

解答

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

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

求解步骤

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

将常数提出:

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

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

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

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

化简

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

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

x \to 0 lim (x - 5)

\frac{d}{d x} (sin (3) (2 x))

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