derivative-7x^4+7x^3-x^2+x

解

導関数

- 7 x^{4} + 7 x^{3} - x^{2} + x

- 28 x^{3} + 21 x^{2} - 2 x + 1

解答ステップ

\frac{d}{d x} (- 7 x^{4} + 7 x^{3} - x^{2} + x)

和/差の法則を適用:

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

= - \frac{d}{d x} (7 x^{4}) + \frac{d}{d x} (7 x^{3}) - \frac{d}{d x} (x^{2}) + \frac{d x}{d x}

\frac{d}{d x} (7 x^{4}) = 28 x^{3}

\frac{d}{d x} (7 x^{3}) = 21 x^{2}

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

\frac{d x}{d x} = 1

= - 28 x^{3} + 21 x^{2} - 2 x + 1