derivative of (2x/(2+sqrt(x)))

解答

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

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

求解步骤

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

将常数提出:

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

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

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

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

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

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

化简

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

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

\int x cos (3 π x^{2}) d x

ln (x) y^{^{'}} = \frac{y}{x}

t an g e n t f (x) = - x, at x = - 4

y^{^{''}} - 8 y^{^{'}} = 4 t

\int \frac{2 x}{x ^{2} - 16} d x