derivative of (x^2/(1+x^3))

解答

\frac{d}{d x} (\frac{x ^{2}}{1 + x ^{3}})

\frac{2 x - x ^{4}}{( 1 + x ^{3} ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x ^{2}}{1 + x ^{3}})

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

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

\frac{d}{d x} (1 + x^{3}) = 3 x^{2}

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

化简

\frac{2 x ( 1 + x ^{3} ) - 3 x ^{2} x ^{2}}{( 1 + x ^{3} ) ^{2}} : \frac{2 x - x ^{4}}{( 1 + x ^{3} ) ^{2}}

= \frac{2 x - x ^{4}}{( 1 + x ^{3} ) ^{2}}

(tan^{3} (x))^{^{'}}

l a pl a ce t r an s f or m 4 t e^{- 2 t}

\frac{d}{d x} (ln (\frac{x ^{2} - 5 ^{2}}{x ^{2} + 5 ^{2}}))

\int (7^{x - 2}) d x

in v erse l a pl a ce \frac{10 s}{s ^{2} + 16}