derivative sin^2(e^{sin(2)(t)})

解

導関数

sin^{2} (e^{s i n (2) (t)})

sin (2) e^{s i n (2) t} sin (2 e^{s i n (2) t})

解答ステップ

\frac{d}{d t} (sin^{2} (e^{s i n (2) t}))

連鎖法則を適用:

2 sin (e^{s i n (2) t}) \frac{d}{d t} (sin (e^{s i n (2) t}))

= 2 sin (e^{s i n (2) t}) \frac{d}{d t} (sin (e^{s i n (2) t}))

\frac{d}{d t} (sin (e^{s i n (2) t})) = cos (e^{s i n (2) t}) e^{s i n (2) t} sin (2)

= 2 sin (e^{s i n (2) t}) cos (e^{s i n (2) t}) e^{s i n (2) t} sin (2)

2倍角の公式を使用:

2 sin (x) cos (x) = sin (2 x)

= sin (2) e^{s i n (2) t} sin (2 e^{s i n (2) t})