derivative of 40x^4+180x^3+240x^2+100x

解

\frac{d}{d x} (40 x^{4} + 180 x^{3} + 240 x^{2} + 100 x)

160 x^{3} + 540 x^{2} + 480 x + 100

解答ステップ

\frac{d}{d x} (40 x^{4} + 180 x^{3} + 240 x^{2} + 100 x)

和/差の法則を適用:

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

= \frac{d}{d x} (40 x^{4}) + \frac{d}{d x} (180 x^{3}) + \frac{d}{d x} (240 x^{2}) + \frac{d}{d x} (100 x)

\frac{d}{d x} (40 x^{4}) = 160 x^{3}

\frac{d}{d x} (180 x^{3}) = 540 x^{2}

\frac{d}{d x} (240 x^{2}) = 480 x

\frac{d}{d x} (100 x) = 100

= 160 x^{3} + 540 x^{2} + 480 x + 100