derivative of (sqrt(x-y)/(2x+4y))

解答

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

\frac{- 5 x \frac{d y}{d x} - x + 2 y \frac{d y}{d x} + 4 y}{( 2 x + 4 y ) ^{2} x - y}

求解步骤

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

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

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

\frac{d}{d x} (2 x + 4 y) = 2 + 4 \frac{d y}{d x}

= \frac{\frac{1 - \frac{d y}{d x}}{2 x - y} ( 2 x + 4 y ) - ( 2 + 4 \frac{d y}{d x} ) x - y}{( 2 x + 4 y ) ^{2}}

化简

\frac{\frac{1 - \frac{d y}{d x}}{2 x - y} ( 2 x + 4 y ) - ( 2 + 4 \frac{d y}{d x} ) x - y}{( 2 x + 4 y ) ^{2}} : \frac{- 5 x \frac{d y}{d x} - x + 2 y \frac{d y}{d x} + 4 y}{( 2 x + 4 y ) ^{2} x - y}

= \frac{- 5 x \frac{d y}{d x} - x + 2 y \frac{d y}{d x} + 4 y}{( 2 x + 4 y ) ^{2} x - y}

s l o p e y - 3 ln (x) - 4 = 0

\int e^{7 x + 6} d x

s l o p e 7 x + 11 (2.5)

\frac{d}{d x} f (x) = \frac{2}{x ^{2}} - 5 x

x \to \frac{π}{2} lim (\frac{x}{2})