derivative sin^4(6x^2)

解

導関数

sin^{4} (6 x^{2})

48 x sin^{3} (6 x^{2}) cos (6 x^{2})

解答ステップ

\frac{d}{d x} (sin^{4} (6 x^{2}))

連鎖法則を適用:

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

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

\frac{d}{d x} (sin (6 x^{2})) = cos (6 x^{2}) \cdot 12 x

= 4 (sin (6 x^{2}))^{3} cos (6 x^{2}) \cdot 12 x

簡素化

= 48 x sin^{3} (6 x^{2}) cos (6 x^{2})