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

解答

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

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

求解步骤

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

使用微分除法定则:

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

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

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

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

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

化简

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

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

\frac{d}{d x} (\frac{x ^{3}}{1 - x ^{3}})

\frac{\partial}{\partial x} (x + e^{z} + y)

\int 4 sin (2 x) - 3 cos (3 x) d x

n or ma l f (x) = x^{4} + 5 x - 2, (1, 4)

\int \frac{e ^{4 r}}{r} d r