derivative-5x^4+5x^3-x^2+x

解

導関数

- 5 x^{4} + 5 x^{3} - x^{2} + x

- 20 x^{3} + 15 x^{2} - 2 x + 1

解答ステップ

\frac{d}{d x} (- 5 x^{4} + 5 x^{3} - x^{2} + x)

和/差の法則を適用:

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

= - \frac{d}{d x} (5 x^{4}) + \frac{d}{d x} (5 x^{3}) - \frac{d}{d x} (x^{2}) + \frac{d x}{d x}

\frac{d}{d x} (5 x^{4}) = 20 x^{3}

\frac{d}{d x} (5 x^{3}) = 15 x^{2}

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

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

= - 20 x^{3} + 15 x^{2} - 2 x + 1