展開する (d^2y)/(d^2x)(x^2+y^2=25)

解

展開する

\frac{d ^{2} y}{d ^{2} x} (x^{2} + y^{2} = 25)

x y + \frac{y ^{3}}{x} = 25

解答ステップ

\frac{d ^{2} y}{d ^{2} x} (x^{2} + y^{2} = 25)

= \frac{d ^{2} y}{d ^{2} x} (x^{2} + 25 = y^{2})

分配法則を適用する:

a (b + c) = ab + a c

a = \frac{d ^{2} y}{d ^{2} x}, b = x^{2}, c = y^{2} = 25

\frac{d ^{2} y}{d ^{2} x} x^{2} + \frac{d ^{2} y}{d ^{2} x} y^{2} = 25

拡張

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

x y + \frac{y ^{3}}{x} = 25