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

解答

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

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

求解步骤

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

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

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

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

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

e x p an d (y^{3} + k x y^{4} - 15 x) d x + (3 x y^{2} + 35 x^{2} y^{3}) d y

e x p an d (2 + 3) (5 + 6)

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

s im pl i f y (p - \frac{2}{q}) (p^{2} + \frac{2 p}{q} + \frac{4}{q ^{2}})

s im pl i f y (a + \frac{1}{6}) (a + \frac{7}{6})