derivative f(x)=[x+(x+sin^2(x))^3]^4

解

導関数

f (x) = [x + (x + sin^{2} (x))^{3}]^{4}

4 (x + (x + sin^{2} (x))^{3})^{3} (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})^{4})

連鎖法則を適用:

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

= 4 (x + (x + sin^{2} (x))^{3})^{3} \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))

= 4 (x + (x + sin^{2} (x))^{3})^{3} (1 + 3 (x + sin^{2} (x))^{2} (1 + sin (2 x)))