derivative (6x+4x^2)/((3+4x)^2)

解答

导数

\frac{6 x + 4 x ^{2}}{( 3 + 4 x ) ^{2}}

\frac{18}{( 3 + 4 x ) ^{3}}

求解步骤

\frac{d}{d x} (\frac{6 x + 4 x ^{2}}{( 3 + 4 x ) ^{2}})

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} ( 6 x + 4 x ^{2} ) ( 3 + 4 x ) ^{2} - \frac{d}{d x} ( ( 3 + 4 x ) ^{2} ) ( 6 x + 4 x ^{2} )}{( ( 3 + 4 x ) ^{2} ) ^{2}}

\frac{d}{d x} (6 x + 4 x^{2}) = 6 + 8 x

\frac{d}{d x} ((3 + 4 x)^{2}) = 8 (3 + 4 x)

= \frac{( 6 + 8 x ) ( 3 + 4 x ) ^{2} - 8 ( 3 + 4 x ) ( 6 x + 4 x ^{2} )}{( ( 3 + 4 x ) ^{2} ) ^{2}}

化简

\frac{( 6 + 8 x ) ( 3 + 4 x ) ^{2} - 8 ( 3 + 4 x ) ( 6 x + 4 x ^{2} )}{( ( 3 + 4 x ) ^{2} ) ^{2}} : \frac{18}{( 3 + 4 x ) ^{3}}

= \frac{18}{( 3 + 4 x ) ^{3}}

y^{^{''}} - y = 1

\frac{d y}{d x} = \frac{8 y ^{2}}{x}

\int 5 e^{- 0.2 x} d x

\frac{\partial}{\partial x} (ln (x - e^{x} y))

y^{^{''}} + 16 y = 8 sin (4 t)