d/(dy)((x)((x^2)/(c^2)-(y^9)/(d^2)))

解

\frac{d}{d y} ((x) (\frac{x ^{2}}{c ^{2}} - \frac{y ^{9}}{d ^{2}}))

- \frac{9 x y ^{8}}{d ^{2}}

解答ステップ

\frac{d}{d y} ((x) (\frac{x ^{2}}{c ^{2}} - \frac{y ^{9}}{d ^{2}}))

c, d, x

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= x \frac{d}{d y} (\frac{x ^{2}}{c ^{2}} - \frac{y ^{9}}{d ^{2}})

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= x (\frac{d}{d y} (\frac{x ^{2}}{c ^{2}}) - \frac{d}{d y} (\frac{y ^{9}}{d ^{2}}))

\frac{d}{d y} (\frac{x ^{2}}{c ^{2}}) = 0

\frac{d}{d y} (\frac{y ^{9}}{d ^{2}}) = \frac{9 y ^{8}}{d ^{2}}

= x (0 - \frac{9 y ^{8}}{d ^{2}})

簡素化

x (0 - \frac{9 y ^{8}}{d ^{2}}) : - \frac{9 x y ^{8}}{d ^{2}}

= - \frac{9 x y ^{8}}{d ^{2}}