derivative (0.1x^2-4.2x+6.5)^{1.5}

解

導関数

(0.1 x^{2} - 4.2 x + 6.5)^{1.5}

1.5 0.1 x^{2} - 4.2 x + 6.5 (0.2 x - 4.2)

解答ステップ

\frac{d}{d x} ((0.1 x^{2} - 4.2 x + 6.5)^{1.5})

連鎖法則を適用:

1.5 0.1 x^{2} - 4.2 x + 6.5 \frac{d}{d x} (0.1 x^{2} - 4.2 x + 6.5)

= 1.5 0.1 x^{2} - 4.2 x + 6.5 \frac{d}{d x} (0.1 x^{2} - 4.2 x + 6.5)

\frac{d}{d x} (0.1 x^{2} - 4.2 x + 6.5) = 0.2 x - 4.2

= 1.5 0.1 x^{2} - 4.2 x + 6.5 (0.2 x - 4.2)