(\partial)/(\partial x)(-5y^4sin(5x))

解

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

- 25 y^{4} cos (5 x)

解答ステップ

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

y

を定数として扱う

定数を除去:

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

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

連鎖法則を適用:

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

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

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

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

簡素化

= - 25 y^{4} cos (5 x)