derivative-5pisin(10pix)

解

導関数

- 5 π sin (10 π x)

- 50 π^{2} cos (10 π x)

解答ステップ

\frac{d}{d x} (- 5 π sin (10 π x))

定数を除去:

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

= - 5 π \frac{d}{d x} (sin (10 π x))

連鎖法則を適用:

cos (10 π x) \frac{d}{d x} (10 π x)

= cos (10 π x) \frac{d}{d x} (10 π x)

\frac{d}{d x} (10 π x) = 10 π

= - 5 π cos (10 π x) \cdot 10 π

簡素化

- 5 π cos (10 π x) \cdot 10 π : - 50 π^{2} cos (10 π x)

= - 50 π^{2} cos (10 π x)