derivative of (2x/(sqrt(1+4x^2)))

解答

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

\frac{2}{( 1 + 4 x ^{2} ) 1 + 4 x ^{2}}

求解步骤

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

将常数提出:

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

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

使用微分除法定则:

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

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

\frac{d x}{d x} = 1

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

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

化简

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

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

x \to 2 lim (a^{2} x + 2 a)

\int \frac{1}{( 1 + 4 y ^{2} )} d y

\frac{d}{d x} (e^{- \frac{1}{2} x})

t a y l or f (x) = x^{3}

\frac{\partial}{\partial x} (4 x y e^{- x^{2} - y^{2}})