(d^2)/(dx^2)((y)(x^2+2y^2-9))

解答

\frac{d ^{2}}{d x ^{2}} ((y) (x^{2} + 2 y^{2} - 9))

x^{2} \frac{d ^{2} y}{d x ^{2}} + 4 x \frac{d y}{d x} + 2 y + 12 y \frac{d y}{d x}^{2} + 6 y^{2} \frac{d ^{2} y}{d x ^{2}} - 9 \frac{d}{d x} (\frac{d y}{d x})

求解步骤

\frac{d ^{2}}{d x ^{2}} ((y) (x^{2} + 2 y^{2} - 9))

\frac{d}{d x} (y (x^{2} + 2 y^{2} - 9)) = x^{2} \frac{d y}{d x} + 2 x y + 6 y^{2} \frac{d y}{d x} - 9 \frac{d y}{d x}

= \frac{d}{d x} (x^{2} \frac{d y}{d x} + 2 x y + 6 y^{2} \frac{d y}{d x} - 9 \frac{d y}{d x})

\frac{d}{d x} (x^{2} \frac{d y}{d x} + 2 x y + 6 y^{2} \frac{d y}{d x} - 9 \frac{d y}{d x}) = x^{2} \frac{d ^{2} y}{d x ^{2}} + 4 x \frac{d y}{d x} + 2 y + 12 y \frac{d y}{d x}^{2} + 6 y^{2} \frac{d ^{2} y}{d x ^{2}} - 9 \frac{d}{d x} (\frac{d y}{d x})

= x^{2} \frac{d ^{2} y}{d x ^{2}} + 4 x \frac{d y}{d x} + 2 y + 12 y \frac{d y}{d x}^{2} + 6 y^{2} \frac{d ^{2} y}{d x ^{2}} - 9 \frac{d}{d x} (\frac{d y}{d x})

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

e x p an d (x - 1 - i) (x - 1 + i)

s im pl i f y (4 + 9 i)^{6}

e x p an d (2 x - y) d x + (4 x + y - 6) d y

s im pl i f y (3 + 4 (y - 2)) (3 - 4 (y - 2))