(\partial)/(\partial x)(10x^3+3x^2y-3y^5)

解

\frac{\partial}{\partial x} (10 x^{3} + 3 x^{2} y - 3 y^{5})

30 x^{2} + 6 x y

解答ステップ

\frac{\partial}{\partial x} (10 x^{3} + 3 x^{2} y - 3 y^{5})

y

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 x} (10 x^{3}) + \frac{\partial}{\partial x} (3 x^{2} y) - \frac{\partial}{\partial x} (3 y^{5})

\frac{\partial}{\partial x} (10 x^{3}) = 30 x^{2}

\frac{\partial}{\partial x} (3 x^{2} y) = 6 y x

\frac{\partial}{\partial x} (3 y^{5}) = 0

= 30 x^{2} + 6 y x - 0

簡素化

= 30 x^{2} + 6 x y