(d^2)/(dx^2)((y)(3x^6+7x^4-2x^2+5))

解答

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

\frac{d ^{2} y}{d x ^{2}} (3 x^{6} + 7 x^{4} - 2 x^{2} + 5) + 2 \frac{d y}{d x} (18 x^{5} + 28 x^{3} - 4 x) + (90 x^{4} + 84 x^{2} - 4) y

求解步骤

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

\frac{d}{d x} (y (3 x^{6} + 7 x^{4} - 2 x^{2} + 5)) = \frac{d y}{d x} (3 x^{6} + 7 x^{4} - 2 x^{2} + 5) + (18 x^{5} + 28 x^{3} - 4 x) y

= \frac{d}{d x} (\frac{d y}{d x} (3 x^{6} + 7 x^{4} - 2 x^{2} + 5) + (18 x^{5} + 28 x^{3} - 4 x) y)

\frac{d}{d x} (\frac{d y}{d x} (3 x^{6} + 7 x^{4} - 2 x^{2} + 5) + (18 x^{5} + 28 x^{3} - 4 x) y) = \frac{d ^{2} y}{d x ^{2}} (3 x^{6} + 7 x^{4} - 2 x^{2} + 5) + 2 \frac{d y}{d x} (18 x^{5} + 28 x^{3} - 4 x) + (90 x^{4} + 84 x^{2} - 4) y

= \frac{d ^{2} y}{d x ^{2}} (3 x^{6} + 7 x^{4} - 2 x^{2} + 5) + 2 \frac{d y}{d x} (18 x^{5} + 28 x^{3} - 4 x) + (90 x^{4} + 84 x^{2} - 4) y

e x p an d - 0.6 (10.3229 - 5)^{2} + 17

e x p an d \frac{2 ( 32 - 771 )}{23}

e x p an d 5 (2 x e^{x} + e^{x} x^{2})

e x p an d (tan (x) - sin (x) sin (y)) d x + cos (x) cos (y) d y

e x p an d \frac{7 s + 1}{( s + 1 ) ( s - 1 )}