derivative (5x^2)/(3x-1)

解答

导数

\frac{5 x ^{2}}{3 x - 1}

\frac{5 ( 3 x ^{2} - 2 x )}{( 3 x - 1 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{5 x ^{2}}{3 x - 1})

将常数提出:

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

= 5 \frac{d}{d x} (\frac{x ^{2}}{3 x - 1})

使用微分除法定则:

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

= 5 \cdot \frac{\frac{d}{d x} ( x ^{2} ) ( 3 x - 1 ) - \frac{d}{d x} ( 3 x - 1 ) x ^{2}}{( 3 x - 1 ) ^{2}}

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

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

= 5 \cdot \frac{2 x ( 3 x - 1 ) - 3 x ^{2}}{( 3 x - 1 ) ^{2}}

化简

5 \cdot \frac{2 x ( 3 x - 1 ) - 3 x ^{2}}{( 3 x - 1 ) ^{2}} : \frac{5 ( 3 x ^{2} - 2 x )}{( 3 x - 1 ) ^{2}}

= \frac{5 ( 3 x ^{2} - 2 x )}{( 3 x - 1 ) ^{2}}

\int_{1}^{2} 3 - \frac{6}{x ^{2}} d x

\int \frac{6 cosh ( x )}{x} d x

y^{^{'''}} + 4 y^{^{''}} - 16 y^{^{'}} - 64 y = 0

\int \frac{3 x ^{2} - x + 1}{x ^{3} - x ^{2}} d x

y^{^{''}} + 49 y = cos (10 t)