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

解答

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

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

求解步骤

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

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

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

化简

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

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

\int 36 (4 x + 4)^{(2)} - 2 (3 x - 1) d x

\int cos^{- 1} (x) d x

t an g e n t x^{2} + 9

\int_{1}^{5} \frac{x ^{2} + 8}{6 x - x ^{2}} d x

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