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

解

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

8 y x^{3} + cos (x^{3}) \cdot 3 x^{2}

解答ステップ

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

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

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

\frac{\partial}{\partial x} (sin (x^{3})) = cos (x^{3}) \cdot 3 x^{2}

= 8 y x^{3} + cos (x^{3}) \cdot 3 x^{2}