derivative of (3x-3/(2sqrt(x)))

解答

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

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

求解步骤

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

将常数提出:

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

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

使用微分除法定则:

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

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

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

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

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

化简

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

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

\frac{d y}{d x} = \frac{3}{1 + x}

f (x) = 3 cos (2 x)

\frac{\partial}{\partial x} (sin (x) - cos (y))

\frac{d}{d x} (arctanh (x))

t a y l or \frac{1}{3 - 2 x}, 1