展開する (d^2)/(d^2x)(x^3+y^3=1)

解

展開する

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

x^{2} + \frac{y ^{3}}{x} = 1

解答ステップ

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

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

分配法則を適用する:

a (b + c) = ab + a c

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

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

拡張

\frac{d ^{2}}{d ^{2} x} x^{3} + \frac{d ^{2}}{d ^{2} x} y^{3} : x^{2} + \frac{y ^{3}}{x}

x^{2} + \frac{y ^{3}}{x} = 1