(d^2)/(dx^2)((y)(4sin(x)+4cos(y)))

解答

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

\frac{d ^{2} y}{d x ^{2}} (4 sin (x) + 4 cos (y)) + 2 (4 cos (x) - 4 sin (y) \frac{d y}{d x}) \frac{d y}{d x} + (- 4 sin (x) - 4 (cos (y) \frac{d y}{d x}^{2} + sin (y) \frac{d ^{2} y}{d x ^{2}})) y

求解步骤

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

\frac{d}{d x} (y (4 sin (x) + 4 cos (y))) = \frac{d y}{d x} (4 sin (x) + 4 cos (y)) + (4 cos (x) - 4 sin (y) \frac{d y}{d x}) y

= \frac{d}{d x} (\frac{d y}{d x} (4 sin (x) + 4 cos (y)) + (4 cos (x) - 4 sin (y) \frac{d y}{d x}) y)

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

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

s im pl i f y t (\frac{10 t}{7} - 20)

e x p an d \frac{2 ( - y + 175 )}{3}

s im pl i f y - b sin (t) + b cos (t) + (1 + b) (1 - b)

e x p an d (3 + 2 i) (1 + 7 i) (= - 11 + 23 i)

s im pl i f y (x + \frac{7}{2}) (x - 3)