(d^2)/(dx^2)((y)(4x^7-5x^2+x))

解

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

\frac{d ^{2} y}{d x ^{2}} (4 x^{7} - 5 x^{2} + x) + 2 \frac{d y}{d x} (28 x^{6} - 10 x + 1) + (168 x^{5} - 10) y

解答ステップ

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

\frac{d}{d x} (y (4 x^{7} - 5 x^{2} + x)) = \frac{d y}{d x} (4 x^{7} - 5 x^{2} + x) + (28 x^{6} - 10 x + 1) y

= \frac{d}{d x} (\frac{d y}{d x} (4 x^{7} - 5 x^{2} + x) + (28 x^{6} - 10 x + 1) y)

\frac{d}{d x} (\frac{d y}{d x} (4 x^{7} - 5 x^{2} + x) + (28 x^{6} - 10 x + 1) y) = \frac{d ^{2} y}{d x ^{2}} (4 x^{7} - 5 x^{2} + x) + 2 \frac{d y}{d x} (28 x^{6} - 10 x + 1) + (168 x^{5} - 10) y

= \frac{d ^{2} y}{d x ^{2}} (4 x^{7} - 5 x^{2} + x) + 2 \frac{d y}{d x} (28 x^{6} - 10 x + 1) + (168 x^{5} - 10) y