derivative of (x^4/(2-x^3))

解答

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

\frac{8 x ^{3} - x ^{6}}{( 2 - x ^{3} ) ^{2}}

求解步骤

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

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

化简

\frac{4 x ^{3} ( 2 - x ^{3} ) - ( - 3 x ^{2} ) x ^{4}}{( 2 - x ^{3} ) ^{2}} : \frac{8 x ^{3} - x ^{6}}{( 2 - x ^{3} ) ^{2}}

= \frac{8 x ^{3} - x ^{6}}{( 2 - x ^{3} ) ^{2}}

\int 216 sin (6 x) 3 cos (6 x) d x

\frac{d}{d x} (csc (x) (x + cot (x)))

d er i v a t i v e 2 sin (x^{2})

x \to \infty lim (- 10 e^{- 2 x})

\frac{d y}{d t} = \frac{y}{2}