(\partial)/(\partial y)(4/3 pi(x^3-y^3))

解

\frac{\partial}{\partial y} (\frac{4}{3} π (x^{3} - y^{3}))

- 4 π y^{2}

解答ステップ

\frac{\partial}{\partial y} (\frac{4}{3} π (x^{3} - y^{3}))

簡素化

\frac{4}{3} π (x^{3} - y^{3}) : \frac{4 π}{3} (x^{3} - y^{3})

= \frac{\partial}{\partial y} (\frac{4 π}{3} (x^{3} - y^{3}))

x

を定数として扱う

定数を除去:

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

= \frac{4 π}{3} \frac{\partial}{\partial y} (x^{3} - y^{3})

和/差の法則を適用:

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

= \frac{4 π}{3} (\frac{\partial}{\partial y} (x^{3}) - \frac{\partial}{\partial y} (y^{3}))

\frac{\partial}{\partial y} (x^{3}) = 0

\frac{\partial}{\partial y} (y^{3}) = 3 y^{2}

= \frac{4 π}{3} (0 - 3 y^{2})

簡素化

\frac{4 π}{3} (0 - 3 y^{2}) : - 4 π y^{2}

= - 4 π y^{2}