(d^3)/(dx^3)((y)(-sin(x)+3x^2-8x+3))

解答

\frac{d ^{3}}{d x ^{3}} ((y) (- sin (x) + 3 x^{2} - 8 x + 3))

3 x^{2} \frac{d ^{3} y}{d x ^{3}} - 8 x \frac{d ^{3} y}{d x ^{3}} + 18 x \frac{d ^{2} y}{d x ^{2}} - sin (x) \frac{d ^{3} y}{d x ^{3}} + 3 \frac{d ^{3} y}{d x ^{3}} - 3 cos (x) \frac{d ^{2} y}{d x ^{2}} - 24 \frac{d ^{2} y}{d x ^{2}} + 3 sin (x) \frac{d y}{d x} + 18 \frac{d y}{d x} + cos (x) y

求解步骤

\frac{d ^{3}}{d x ^{3}} ((y) (- sin (x) + 3 x^{2} - 8 x + 3))

\frac{d}{d x} (y (- sin (x) + 3 x^{2} - 8 x + 3)) = \frac{d y}{d x} (- sin (x) + 3 x^{2} - 8 x + 3) + (6 x - cos (x) - 8) y

= \frac{d ^{2}}{d x ^{2}} (\frac{d y}{d x} (- sin (x) + 3 x^{2} - 8 x + 3) + (6 x - cos (x) - 8) y)

\frac{d}{d x} (\frac{d y}{d x} (- sin (x) + 3 x^{2} - 8 x + 3) + (6 x - cos (x) - 8) y) = \frac{d ^{2} y}{d x ^{2}} (- sin (x) + 3 x^{2} - 8 x + 3) + 2 \frac{d y}{d x} (6 x - cos (x) - 8) + (sin (x) + 6) y

= \frac{d}{d x} (\frac{d ^{2} y}{d x ^{2}} (- sin (x) + 3 x^{2} - 8 x + 3) + 2 \frac{d y}{d x} (6 x - cos (x) - 8) + (sin (x) + 6) y)

\frac{d}{d x} (\frac{d ^{2} y}{d x ^{2}} (- sin (x) + 3 x^{2} - 8 x + 3) + 2 \frac{d y}{d x} (6 x - cos (x) - 8) + (sin (x) + 6) y) = 3 x^{2} \frac{d ^{3} y}{d x ^{3}} - 8 x \frac{d ^{3} y}{d x ^{3}} + 18 x \frac{d ^{2} y}{d x ^{2}} - sin (x) \frac{d ^{3} y}{d x ^{3}} + 3 \frac{d ^{3} y}{d x ^{3}} - 3 cos (x) \frac{d ^{2} y}{d x ^{2}} - 24 \frac{d ^{2} y}{d x ^{2}} + 3 sin (x) \frac{d y}{d x} + 18 \frac{d y}{d x} + cos (x) y

= 3 x^{2} \frac{d ^{3} y}{d x ^{3}} - 8 x \frac{d ^{3} y}{d x ^{3}} + 18 x \frac{d ^{2} y}{d x ^{2}} - sin (x) \frac{d ^{3} y}{d x ^{3}} + 3 \frac{d ^{3} y}{d x ^{3}} - 3 cos (x) \frac{d ^{2} y}{d x ^{2}} - 24 \frac{d ^{2} y}{d x ^{2}} + 3 sin (x) \frac{d y}{d x} + 18 \frac{d y}{d x} + cos (x) y

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

e x p an d 3 x^{3} (- ln (x) + c)

s im pl i f y 2 (83 + 37)

s im pl i f y q (20 - \frac{q}{30})

e x p an d (x - 35) (x + 35)