d/(dy)((x)(sin(5x)))

解

\frac{d}{d y} ((y) (sin (5 y)))

sin (5 y) + 5 y cos (5 y)

解答ステップ

\frac{d}{d y} ((y) (sin (5 y)))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = sin (5 y)

= \frac{d y}{d y} sin (5 y) + \frac{d}{d y} (sin (5 y)) y

\frac{d y}{d y} = 1

\frac{d}{d y} (sin (5 y)) = cos (5 y) \cdot 5

= 1 \cdot sin (5 y) + cos (5 y) \cdot 5 y

簡素化

= sin (5 y) + 5 y cos (5 y)