derivative f(x)=(x^3)/(6x-3)

解答

导数

f (x) = \frac{x ^{3}}{6 x - 3}

\frac{x ^{2} ( 4 x - 3 )}{3 ( 2 x - 1 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x ^{3}}{6 x - 3})

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} ( x ^{3} ) ( 6 x - 3 ) - \frac{d}{d x} ( 6 x - 3 ) x ^{3}}{( 6 x - 3 ) ^{2}}

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

\frac{d}{d x} (6 x - 3) = 6

= \frac{3 x ^{2} ( 6 x - 3 ) - 6 x ^{3}}{( 6 x - 3 ) ^{2}}

化简

\frac{3 x ^{2} ( 6 x - 3 ) - 6 x ^{3}}{( 6 x - 3 ) ^{2}} : \frac{x ^{2} ( 4 x - 3 )}{3 ( 2 x - 1 ) ^{2}}

= \frac{x ^{2} ( 4 x - 3 )}{3 ( 2 x - 1 ) ^{2}}

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

\frac{d y}{d t} = \frac{t ^{2} + t y + y ^{2}}{t ^{2}}

n = 0 \sum \infty n (n + 1)

\int_{4}^{9} \frac{1}{x ^{2} - 1} d x

\int_{0}^{1} 4 e^{7 x} d x