derivative of (x-7/(x+2))

解答

\frac{d}{d x} (\frac{x - 7}{x + 2})

\frac{9}{( x + 2 ) ^{2}}

求解步骤

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

\frac{d}{d x} (x - 7) = 1

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

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

化简

\frac{1 \cdot ( x + 2 ) - 1 \cdot ( x - 7 )}{( x + 2 ) ^{2}} : \frac{9}{( x + 2 ) ^{2}}

= \frac{9}{( x + 2 ) ^{2}}

\frac{d}{d x} (4 x - 2 y)

\frac{d y}{d x} - 2 x y = 6 x, y (0) = - 7

\frac{d}{d x} (7 - \frac{4}{x - 8} + \frac{2 x}{3 x + 1})

\int \frac{31}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

\int tan (6 x + 1) d x