derivative (y^3)/(27)+9/(4y)

解

導関数

\frac{y ^{3}}{27} + \frac{9}{4 y}

\frac{y ^{2}}{9} - \frac{9}{4 y ^{2}}

解答ステップ

\frac{d}{d y} (\frac{y ^{3}}{27} + \frac{9}{4 y})

和/差の法則を適用:

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

= \frac{d}{d y} (\frac{y ^{3}}{27}) + \frac{d}{d y} (\frac{9}{4 y})

\frac{d}{d y} (\frac{y ^{3}}{27}) = \frac{y ^{2}}{9}

\frac{d}{d y} (\frac{9}{4 y}) = - \frac{9}{4 y ^{2}}

= \frac{y ^{2}}{9} - \frac{9}{4 y ^{2}}