derivative of 80picos(10pix)

解

\frac{d}{d x} (80 π cos (10 π x))

- 800 π^{2} sin (10 π x)

解答ステップ

\frac{d}{d x} (80 π cos (10 π x))

定数を除去:

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

= 80 π \frac{d}{d x} (cos (10 π x))

連鎖法則を適用:

- sin (10 π x) \frac{d}{d x} (10 π x)

= - sin (10 π x) \frac{d}{d x} (10 π x)

\frac{d}{d x} (10 π x) = 10 π

= 80 π (- sin (10 π x) \cdot 10 π)

簡素化

80 π (- sin (10 π x) \cdot 10 π) : - 800 π^{2} sin (10 π x)

= - 800 π^{2} sin (10 π x)