derivative f(x)=x^4-3x^3-9x^2+5x

解

導関数

f (x) = x^{4} - 3 x^{3} - 9 x^{2} + 5 x

4 x^{3} - 9 x^{2} - 18 x + 5

解答ステップ

\frac{d}{d x} (x^{4} - 3 x^{3} - 9 x^{2} + 5 x)

和/差の法則を適用:

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

= \frac{d}{d x} (x^{4}) - \frac{d}{d x} (3 x^{3}) - \frac{d}{d x} (9 x^{2}) + \frac{d}{d x} (5 x)

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

\frac{d}{d x} (3 x^{3}) = 9 x^{2}

\frac{d}{d x} (9 x^{2}) = 18 x

\frac{d}{d x} (5 x) = 5

= 4 x^{3} - 9 x^{2} - 18 x + 5