(\partial)/(\partial y)(1+x^4+y^3)

解

\frac{\partial}{\partial y} (1 + x^{4} + y^{3})

3 y^{2}

解答ステップ

\frac{\partial}{\partial y} (1 + x^{4} + y^{3})

x

を定数として扱う

和/差の法則を適用:

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

= \frac{\partial}{\partial y} (1) + \frac{\partial}{\partial y} (x^{4}) + \frac{\partial}{\partial y} (y^{3})

\frac{\partial}{\partial y} (1) = 0

\frac{\partial}{\partial y} (x^{4}) = 0

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

= 0 + 0 + 3 y^{2}

簡素化

= 3 y^{2}