(d^2)/(dx^2)((y)(3x^2+5e^x))

解

\frac{d ^{2}}{d x ^{2}} ((y) (3 x^{2} + 5 e^{x}))

\frac{d ^{2} y}{d x ^{2}} (3 x^{2} + 5 e^{x}) + 2 \frac{d y}{d x} (6 x + 5 e^{x}) + (6 + 5 e^{x}) y

解答ステップ

\frac{d ^{2}}{d x ^{2}} ((y) (3 x^{2} + 5 e^{x}))

\frac{d}{d x} (y (3 x^{2} + 5 e^{x})) = \frac{d y}{d x} (3 x^{2} + 5 e^{x}) + (6 x + 5 e^{x}) y

= \frac{d}{d x} (\frac{d y}{d x} (3 x^{2} + 5 e^{x}) + (6 x + 5 e^{x}) y)

\frac{d}{d x} (\frac{d y}{d x} (3 x^{2} + 5 e^{x}) + (6 x + 5 e^{x}) y) = \frac{d ^{2} y}{d x ^{2}} (3 x^{2} + 5 e^{x}) + 2 \frac{d y}{d x} (6 x + 5 e^{x}) + (6 + 5 e^{x}) y

= \frac{d ^{2} y}{d x ^{2}} (3 x^{2} + 5 e^{x}) + 2 \frac{d y}{d x} (6 x + 5 e^{x}) + (6 + 5 e^{x}) y