(\partial)/(\partial x)(y^4cos(4x)*4)

解

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

- 16 y^{4} sin (4 x)

解答ステップ

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

y

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= y^{4} \cdot 4 \frac{\partial}{\partial x} (cos (4 x))

連鎖法則を適用:

- sin (4 x) \frac{\partial}{\partial x} (4 x)

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

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

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

簡素化

= - 16 y^{4} sin (4 x)