(\partial)/(\partial x)(3x^4-sin(5x)+4x)

解

\frac{\partial}{\partial x} (3 x^{4} - sin (5 x) + 4 x)

12 x^{3} - cos (5 x) \cdot 5 + 4

解答ステップ

\frac{\partial}{\partial x} (3 x^{4} - sin (5 x) + 4 x)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (3 x^{4}) - \frac{\partial}{\partial x} (sin (5 x)) + \frac{\partial}{\partial x} (4 x)

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

\frac{\partial}{\partial x} (sin (5 x)) = cos (5 x) \cdot 5

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

= 12 x^{3} - cos (5 x) \cdot 5 + 4