derivative of x^4+4/3 x^3-4x^2

解答

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

4 x^{3} + 4 x^{2} - 8 x

求解步骤

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

化简

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

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

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

\frac{d}{d x} (4 x^{2}) = 8 x

= 4 x^{3} + 4 x^{2} - 8 x

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

x \to 0 lim (\frac{7 e ^{x}}{x ^{5}})

\int 4 x^{2} - 2 d x

x \to + 1 lim (0)

in v erse l a pl a ce \frac{x}{( x ^{2} - 9 ) \cdot x}