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

解答

\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

求解步骤

\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

e x p an d \frac{( - s ^{3} - A \cdot s ^{2} - 3 s - 4 A )}{( ( s ^{2} + 4 ) ( s ^{2} + 9 ) )}

e x p an d (3 x^{2} + 2 x y + 4 y^{2}) d x

s im pl i f y 0.00646 (\frac{12.5}{s} + 1)

e x p an d (- 6, - 5) y (- 4, - 4)

s im pl i f y (2 + 2 x - 5)^{2}