derivative of (2+(x^2+1^4)^3)

解

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

3 (x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 3)^{2} (8 x^{7} + 24 x^{5} + 24 x^{3} + 8 x)

解答ステップ

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

簡素化

(2 + (x^{2} + 1)^{4})^{3} : (x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 3)^{3}

= \frac{d}{d x} ((x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 3)^{3})

連鎖法則を適用:

3 (x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 3)^{2} \frac{d}{d x} (x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 3)

= 3 (x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 3)^{2} \frac{d}{d x} (x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 3)

\frac{d}{d x} (x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 3) = 8 x^{7} + 24 x^{5} + 24 x^{3} + 8 x

= 3 (x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 3)^{2} (8 x^{7} + 24 x^{5} + 24 x^{3} + 8 x)