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

解答

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

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

求解步骤

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

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

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

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

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

化简

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

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

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

d er i v a t i v e x - 4

a re a y = sin (x), y = 3 x, x = \frac{π}{2}, x = π

\frac{d}{d x} (3 x^{3} + 6 x + 7)

d er i v a t i v e f (x) = \frac{- 4}{x ^{3}}