(\partial)/(\partial x)(y^4cos(5x))

解

\frac{\partial}{\partial x} (y^{4} cos (5 x))

- 5 y^{4} sin (5 x)

解答ステップ

\frac{\partial}{\partial x} (y^{4} cos (5 x))

y

を定数として扱う

定数を除去:

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

= y^{4} \frac{\partial}{\partial x} (cos (5 x))

連鎖法則を適用:

- sin (5 x) \frac{\partial}{\partial x} (5 x)

= - sin (5 x) \frac{\partial}{\partial x} (5 x)

\frac{\partial}{\partial x} (5 x) = 5

= y^{4} (- sin (5 x) \cdot 5)

簡素化

= - 5 y^{4} sin (5 x)