derivative (3x-7)/(sqrt(x))

解答

导数

\frac{3 x - 7}{x}

\frac{3 x + 7}{2 x x}

求解步骤

\frac{d}{d x} (\frac{3 x - 7}{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} ( 3 x - 7 ) x - \frac{d}{d x} ( x ) ( 3 x - 7 )}{( x ) ^{2}}

\frac{d}{d x} (3 x - 7) = 3

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

= \frac{3 x - \frac{1}{2 x} ( 3 x - 7 )}{( x ) ^{2}}

化简

\frac{3 x - \frac{1}{2 x} ( 3 x - 7 )}{( x ) ^{2}} : \frac{3 x + 7}{2 x x}

= \frac{3 x + 7}{2 x x}

\int \frac{1}{x} sin (x) d x

s l o p e y = 4 x - 3 x^{2}, (2, - 4)

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