derivative of [x+(x+sin^2(x)^3]^6)

解

\frac{d}{d x} ([x + (x + sin^{2} (x))^{3}]^{6})

6 (x + (x + sin^{2} (x))^{3})^{5} (1 + 3 (x + sin^{2} (x))^{2} (1 + sin (2 x)))

解答ステップ

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

連鎖法則を適用:

6 (x + (x + sin^{2} (x))^{3})^{5} \frac{d}{d x} (x + (x + sin^{2} (x))^{3})

= 6 (x + (x + sin^{2} (x))^{3})^{5} \frac{d}{d x} (x + (x + sin^{2} (x))^{3})

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

= 6 (x + (x + sin^{2} (x))^{3})^{5} (1 + 3 (x + sin^{2} (x))^{2} (1 + sin (2 x)))