derivative of (1+2x+3x^2+4x^3^{100})

解

\frac{d}{d x} ((1 + 2 x + 3 x^{2} + 4 x^{3})^{100})

100 (1 + 2 x + 3 x^{2} + 4 x^{3})^{99} (12 x^{2} + 6 x + 2)

解答ステップ

\frac{d}{d x} ((1 + 2 x + 3 x^{2} + 4 x^{3})^{100})

連鎖法則を適用:

100 (1 + 2 x + 3 x^{2} + 4 x^{3})^{99} \frac{d}{d x} (1 + 2 x + 3 x^{2} + 4 x^{3})

= 100 (1 + 2 x + 3 x^{2} + 4 x^{3})^{99} \frac{d}{d x} (1 + 2 x + 3 x^{2} + 4 x^{3})

\frac{d}{d x} (1 + 2 x + 3 x^{2} + 4 x^{3}) = 12 x^{2} + 6 x + 2

= 100 (1 + 2 x + 3 x^{2} + 4 x^{3})^{99} (12 x^{2} + 6 x + 2)