(d^2)/(dx^2)((cos(2x))(sin(6x)))

解

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

- 40 sin (6 x) cos (2 x) - 24 cos (6 x) sin (2 x)

解答ステップ

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

\frac{d}{d x} (cos (2 x) sin (6 x)) = - 2 sin (2 x) sin (6 x) + 6 cos (6 x) cos (2 x)

= \frac{d}{d x} (- 2 sin (2 x) sin (6 x) + 6 cos (6 x) cos (2 x))

\frac{d}{d x} (- 2 sin (2 x) sin (6 x) + 6 cos (6 x) cos (2 x)) = - 40 sin (6 x) cos (2 x) - 24 cos (6 x) sin (2 x)

= - 40 sin (6 x) cos (2 x) - 24 cos (6 x) sin (2 x)