derivative of (x^2+2x/(3x+6))

解答

\frac{d}{d x} (\frac{x ^{2} + 2 x}{3 x + 6})

\frac{1}{3}

十进制

0.33333 \dots

求解步骤

\frac{d}{d x} (\frac{x ^{2} + 2 x}{3 x + 6})

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 ^{2} + 2 x ) ( 3 x + 6 ) - \frac{d}{d x} ( 3 x + 6 ) ( x ^{2} + 2 x )}{( 3 x + 6 ) ^{2}}

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

\frac{d}{d x} (3 x + 6) = 3

= \frac{( 2 x + 2 ) ( 3 x + 6 ) - 3 ( x ^{2} + 2 x )}{( 3 x + 6 ) ^{2}}

化简

\frac{( 2 x + 2 ) ( 3 x + 6 ) - 3 ( x ^{2} + 2 x )}{( 3 x + 6 ) ^{2}} : \frac{1}{3}

= \frac{1}{3}

x \to - 1 lim (x^{3} - 2)

p a r i t y cot^{2} (sin (θ))

x \to 0 lim (\frac{x ^{2} + x}{x ^{2}})

l a pl a ce t r an s f or m - 6 t^{2}

\frac{\partial}{\partial x} (x \cdot y - x \cdot y)