derivative of (3x^2/(ln(x)))

解答

\frac{d}{d x} (\frac{3 x ^{2}}{ln ( x )})

\frac{3 ( 2 x ln ( x ) - x )}{ln ^{2} ( x )}

求解步骤

\frac{d}{d x} (\frac{3 x ^{2}}{ln ( x )})

将常数提出:

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

= 3 \frac{d}{d x} (\frac{x ^{2}}{ln ( x )})

使用微分除法定则:

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

= 3 \cdot \frac{\frac{d}{d x} ( x ^{2} ) ln ( x ) - \frac{d}{d x} ( ln ( x ) ) x ^{2}}{( ln ( x ) ) ^{2}}

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

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

= 3 \cdot \frac{2 x ln ( x ) - \frac{1}{x} x ^{2}}{( ln ( x ) ) ^{2}}

化简

3 \cdot \frac{2 x ln ( x ) - \frac{1}{x} x ^{2}}{ln ^{2} ( x )} : \frac{3 ( 2 x ln ( x ) - x )}{ln ^{2} ( x )}

= \frac{3 ( 2 x ln ( x ) - x )}{ln ^{2} ( x )}

\frac{d y}{d x} = (x + y)^{2} - 1, y (3) = 4

\int_{0}^{1} 2 (1 + x)^{8} d x

d er i v a t i v e \frac{( x + 2 )}{( x - 2 )}

x \to 3 lim (\frac{2 ^{x} - 8}{3 - x})

a re a y = 4 x, y = 4, y = \frac{4}{9} x^{2} 4