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

解

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

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

解答ステップ

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

簡素化

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})

和/差の法則を適用:

(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