(d^2)/(dx^2)((y)(sin(x)+cos(x)))

解

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

\frac{d ^{2} y}{d x ^{2}} (sin (x) + cos (x)) + 2 (cos (x) - sin (x)) \frac{d y}{d x} + (- sin (x) - cos (x)) y

解答ステップ

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

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

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

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

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