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

解

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

6 y x^{2} - sin (x^{4}) \cdot 4 x^{3}

解答ステップ

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

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

\frac{\partial}{\partial x} (2 x^{3} y) = 6 y x^{2}

\frac{\partial}{\partial x} (cos (x^{4})) = - sin (x^{4}) \cdot 4 x^{3}

= 6 y x^{2} - sin (x^{4}) \cdot 4 x^{3}