(\partial)/(\partial x)(5x^4+2xy+1)

解

\frac{\partial}{\partial x} (5 x^{4} + 2 x y + 1)

20 x^{3} + 2 y

解答ステップ

\frac{\partial}{\partial x} (5 x^{4} + 2 x y + 1)

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} (5 x^{4}) + \frac{\partial}{\partial x} (2 x y) + \frac{\partial}{\partial x} (1)

\frac{\partial}{\partial x} (5 x^{4}) = 20 x^{3}

\frac{\partial}{\partial x} (2 x y) = 2 y

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

= 20 x^{3} + 2 y + 0

簡素化

= 20 x^{3} + 2 y