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

解

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

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

解答ステップ

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

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

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

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

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