d/(dt)(cos^2(e^{cos^2(t)}))

解

\frac{d}{d t} (cos^{2} (e^{c o s^{2} (t)}))

e^{c o s^{2} (t)} sin (2 e^{c o s^{2} (t)}) sin (2 t)

解答ステップ

\frac{d}{d t} (cos^{2} (e^{c o s^{2} (t)}))

連鎖法則を適用:

2 cos (e^{c o s^{2} (t)}) \frac{d}{d t} (cos (e^{c o s^{2} (t)}))

= 2 cos (e^{c o s^{2} (t)}) \frac{d}{d t} (cos (e^{c o s^{2} (t)}))

\frac{d}{d t} (cos (e^{c o s^{2} (t)})) = e^{c o s^{2} (t)} sin (e^{c o s^{2} (t)}) sin (2 t)

= 2 cos (e^{c o s^{2} (t)}) e^{c o s^{2} (t)} sin (e^{c o s^{2} (t)}) sin (2 t)

2倍角の公式を使用:

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

= e^{c o s^{2} (t)} sin (2 e^{c o s^{2} (t)}) sin (2 t)