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

解答

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

x^{2} \frac{d ^{2} y}{d x ^{2}} + 4 x \frac{d y}{d x} + 2 y - 4 \frac{d y}{d x}^{2} - 4 y \frac{d ^{2} y}{d x ^{2}}

求解步骤

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

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

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

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

= x^{2} \frac{d ^{2} y}{d x ^{2}} + 4 x \frac{d y}{d x} + 2 y - 4 \frac{d y}{d x}^{2} - 4 y \frac{d ^{2} y}{d x ^{2}}

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

s im pl i f y (x + 3) (x - 3)

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

e x p an d 2 (11 + 3)

e x p an d (e^{3 x} + e^{- 3 x})^{2}