(d^2}{dx^2}((y)(\frac{4x^5)/5-7x))

解

\frac{d ^{2}}{d x ^{2}} ((y) (\frac{4 x ^{5}}{5} - 7 x))

\frac{d ^{2} y}{d x ^{2}} (\frac{4 x ^{5}}{5} - 7 x) + 2 \frac{d y}{d x} (4 x^{4} - 7) + 16 x^{3} y

解答ステップ

\frac{d ^{2}}{d x ^{2}} ((y) (\frac{4 x ^{5}}{5} - 7 x))

\frac{d}{d x} (y (\frac{4 x ^{5}}{5} - 7 x)) = \frac{d y}{d x} (\frac{4 x ^{5}}{5} - 7 x) + (4 x^{4} - 7) y

= \frac{d}{d x} (\frac{d y}{d x} (\frac{4 x ^{5}}{5} - 7 x) + (4 x^{4} - 7) y)

\frac{d}{d x} (\frac{d y}{d x} (\frac{4 x ^{5}}{5} - 7 x) + (4 x^{4} - 7) y) = \frac{d ^{2} y}{d x ^{2}} (\frac{4 x ^{5}}{5} - 7 x) + 2 \frac{d y}{d x} (4 x^{4} - 7) + 16 x^{3} y

= \frac{d ^{2} y}{d x ^{2}} (\frac{4 x ^{5}}{5} - 7 x) + 2 \frac{d y}{d x} (4 x^{4} - 7) + 16 x^{3} y