展開する (d^2x)/(d^2y)(4y^3=6x^2+1)

解

展開する

\frac{d ^{2} x}{d ^{2} y} (4 y^{3} = 6 x^{2} + 1)

4 x y^{2} = 6 x^{2} + \frac{x}{y}

解答ステップ

\frac{d ^{2} x}{d ^{2} y} (4 y^{3} = 6 x^{2} + 1)

= \frac{d ^{2} x}{d ^{2} y} (4 \cdot 6 = x^{2} y^{3} + 1)

分配法則を適用する:

a (b + c) = ab + a c

a = \frac{d ^{2} x}{d ^{2} y}, b = 4 y^{3} = 6 x^{2}, c = 1

\frac{d ^{2} x}{d ^{2} y} \cdot 4 y^{3} = 6 x^{2} + \frac{d ^{2} x}{d ^{2} y} \cdot 1

4 \cdot \frac{d ^{2} x}{d ^{2} y} y^{3} = 6 x^{2} + 1 \cdot \frac{d ^{2} x}{d ^{2} y}

簡素化

4 \cdot \frac{d ^{2} x}{d ^{2} y} y^{3} = 6 x^{2} + 1 \cdot \frac{d ^{2} x}{d ^{2} y} : 4 x y^{2} = 6 x^{2} + \frac{x}{y}

4 x y^{2} = 6 x^{2} + \frac{x}{y}