(d^2)/(dx^2)((y)(2x^3-4x^2+7x-5))

解答

\frac{d ^{2}}{d x ^{2}} ((y) (2 x^{3} - 4 x^{2} + 7 x - 5))

\frac{d ^{2} y}{d x ^{2}} (2 x^{3} - 4 x^{2} + 7 x - 5) + 2 (6 x^{2} - 8 x + 7) \frac{d y}{d x} + (12 x - 8) y

求解步骤

\frac{d ^{2}}{d x ^{2}} ((y) (2 x^{3} - 4 x^{2} + 7 x - 5))

\frac{d}{d x} (y (2 x^{3} - 4 x^{2} + 7 x - 5)) = \frac{d y}{d x} (2 x^{3} - 4 x^{2} + 7 x - 5) + (6 x^{2} - 8 x + 7) y

= \frac{d}{d x} (\frac{d y}{d x} (2 x^{3} - 4 x^{2} + 7 x - 5) + (6 x^{2} - 8 x + 7) y)

\frac{d}{d x} (\frac{d y}{d x} (2 x^{3} - 4 x^{2} + 7 x - 5) + (6 x^{2} - 8 x + 7) y) = \frac{d ^{2} y}{d x ^{2}} (2 x^{3} - 4 x^{2} + 7 x - 5) + 2 (6 x^{2} - 8 x + 7) \frac{d y}{d x} + (12 x - 8) y

= \frac{d ^{2} y}{d x ^{2}} (2 x^{3} - 4 x^{2} + 7 x - 5) + 2 (6 x^{2} - 8 x + 7) \frac{d y}{d x} + (12 x - 8) y

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

e x p an d \frac{450 ( 16 x - 8 )}{8 x ^{2} - 8 x + 5}

e x p an d \frac{2 ω ( ω ^{2} - 4 )}{- 7 ω ^{2} + 3}

e x p an d \frac{( s + 1 )}{( s ^{2} - 4 ) ( s + 5 )}

e x p an d \frac{- 3 x ^{2} + 2 x + 12}{( x - 2 ) ( x + 2 ) ( x + 1 )}