(d^2)/(dx^2)((5x^2+4x)cos(x))

解

\frac{d ^{2}}{d x ^{2}} ((5 x^{2} + 4 x) cos (x))

- 5 x^{2} cos (x) - 20 x sin (x) - 4 x cos (x) - 8 sin (x) + 10 cos (x)

解答ステップ

\frac{d ^{2}}{d x ^{2}} ((5 x^{2} + 4 x) cos (x))

\frac{d}{d x} ((5 x^{2} + 4 x) cos (x)) = cos (x) (10 x + 4) - sin (x) (5 x^{2} + 4 x)

= \frac{d}{d x} (cos (x) (10 x + 4) - sin (x) (5 x^{2} + 4 x))

\frac{d}{d x} (cos (x) (10 x + 4) - sin (x) (5 x^{2} + 4 x)) = - 5 x^{2} cos (x) - 20 x sin (x) - 4 x cos (x) - 8 sin (x) + 10 cos (x)

= - 5 x^{2} cos (x) - 20 x sin (x) - 4 x cos (x) - 8 sin (x) + 10 cos (x)