(\partial)/(\partial x)(4x^2y^3+1)

解

\frac{\partial}{\partial x} (4 x^{2} y^{3} + 1)

8 x y^{3}

解答ステップ

\frac{\partial}{\partial x} (4 x^{2} y^{3} + 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} (4 x^{2} y^{3}) + \frac{\partial}{\partial x} (1)

\frac{\partial}{\partial x} (4 x^{2} y^{3}) = 8 y^{3} x

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

= 8 y^{3} x + 0

簡素化

= 8 x y^{3}