derivative (4x-3)/(sqrt(x))

解答

导数

\frac{4 x - 3}{x}

\frac{4 x + 3}{2 x x}

求解步骤

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

\frac{d}{d x} (4 x - 3) = 4

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

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

化简

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

= \frac{4 x + 3}{2 x x}

y^{^{''}} - \frac{3}{x} y^{^{'}} - \frac{4}{x ^{2}} y = 0

\frac{\partial}{\partial x} (17 x^{3} y^{2})

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

\frac{d y}{d x} = \frac{y sin ( x )}{1 - 2 y}

y^{^{'}} = e^{y - x}, y (0) = 0