derivative of 1.2sin(2x-0.8*t+10)

解

\frac{d}{d x} (1.2 \cdot sin (2 \cdot x - 0.8 \cdot t + 10))

2.4 cos (2 x - 0.8 t + 10)

解答ステップ

\frac{d}{d x} (1.2 sin (2 x - 0.8 t + 10))

t

を定数として扱う

定数を除去:

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

= 1.2 \frac{d}{d x} (sin (2 x - 0.8 t + 10))

連鎖法則を適用:

cos (2 x - 0.8 t + 10) \frac{d}{d x} (2 x - 0.8 t + 10)

= cos (2 x - 0.8 t + 10) \frac{d}{d x} (2 x - 0.8 t + 10)

\frac{d}{d x} (2 x - 0.8 t + 10) = 2

= 1.2 cos (2 x - 0.8 t + 10) \cdot 2

簡素化

= 2.4 cos (2 x - 0.8 t + 10)