(\partial)/(\partial x)(x(2x-y^3))

解

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

4 x - y^{3}

解答ステップ

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

y

を定数として扱う

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 2 x - y^{3}

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

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

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

= 1 \cdot (2 x - y^{3}) + 2 x

簡素化

= 4 x - y^{3}