(\partial)/(\partial x)(4x-3x^4y^2)

解

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

4 - 12 y^{2} x^{3}

解答ステップ

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

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

\frac{\partial}{\partial x} (4 x) = 4

\frac{\partial}{\partial x} (3 x^{4} y^{2}) = 12 y^{2} x^{3}

= 4 - 12 y^{2} x^{3}