展開する (7x^2+1)*(d^2y)/(dx^2)

解

展開する

(7 x^{2} + 1) \cdot \frac{d ^{2} y}{d x ^{2}}

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

解答ステップ

(7 x^{2} + 1) \frac{d ^{2} y}{d x ^{2}}

分配法則を適用する:

a (b + c) = ab + a c

a = \frac{d ^{2} y}{d x ^{2}}, b = 7 x^{2}, c = 1

= \frac{d ^{2} y}{d x ^{2}} 7 x^{2} + \frac{d ^{2} y}{d x ^{2}} 1

= 7 x^{2} \frac{d ^{2} y}{d x ^{2}} + 1 \frac{d ^{2} y}{d x ^{2}}

乗算:

1 \frac{d ^{2} y}{d x ^{2}} = \frac{d ^{2} y}{d x ^{2}}

= 7 x^{2} \frac{d ^{2} y}{d x ^{2}} + \frac{d ^{2} y}{d x ^{2}}