(d^2)/(dx^2)((y)(xsin(x)-cos(x)))

解

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

\frac{d ^{2} y}{d x ^{2}} (x sin (x) - cos (x)) + 2 \frac{d y}{d x} (x cos (x) + 2 sin (x)) + (- x sin (x) + 3 cos (x)) y

解答ステップ

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

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

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

\frac{d}{d x} (\frac{d y}{d x} (x sin (x) - cos (x)) + (x cos (x) + 2 sin (x)) y) = \frac{d ^{2} y}{d x ^{2}} (x sin (x) - cos (x)) + 2 \frac{d y}{d x} (x cos (x) + 2 sin (x)) + (- x sin (x) + 3 cos (x)) y

= \frac{d ^{2} y}{d x ^{2}} (x sin (x) - cos (x)) + 2 \frac{d y}{d x} (x cos (x) + 2 sin (x)) + (- x sin (x) + 3 cos (x)) y