d/(dy)((y/8)^4+1/(4y^2))

解

\frac{d}{d y} ((\frac{y}{8})^{4} + \frac{1}{4 y ^{2}})

\frac{y ^{3}}{1024} - \frac{1}{2 y ^{3}}

解答ステップ

\frac{d}{d y} ((\frac{y}{8})^{4} + \frac{1}{4 y ^{2}})

簡素化

(\frac{y}{8})^{4} + \frac{1}{4 y ^{2}} : \frac{y ^{4}}{4096} + \frac{1}{4 y ^{2}}

= \frac{d}{d y} (\frac{y ^{4}}{4096} + \frac{1}{4 y ^{2}})

和/差の法則を適用:

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

= \frac{d}{d y} (\frac{y ^{4}}{4096}) + \frac{d}{d y} (\frac{1}{4 y ^{2}})

\frac{d}{d y} (\frac{y ^{4}}{4096}) = \frac{y ^{3}}{1024}

\frac{d}{d y} (\frac{1}{4 y ^{2}}) = - \frac{1}{2 y ^{3}}

= \frac{y ^{3}}{1024} - \frac{1}{2 y ^{3}}