(d^2)/(dx^2)((y)(e^{2x}-kx))

解

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

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

解答ステップ

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

\frac{d}{d x} (y (e^{2 x} - k x)) = \frac{d y}{d x} (e^{2 x} - k x) + (e^{2 x} \cdot 2 - k) y

= \frac{d}{d x} (\frac{d y}{d x} (e^{2 x} - k x) + (e^{2 x} \cdot 2 - k) y)

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

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