d/(dy)((x)(1+sin((pix)/4)))

解

\frac{d}{d y} ((y) (1 + sin (\frac{π y}{4})))

1 + sin (\frac{π y}{4}) + \frac{π y cos ( \frac{π y}{4} )}{4}

解答ステップ

\frac{d}{d y} ((y) (1 + sin (\frac{π y}{4})))

積の法則を適用:

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

f = y, g = 1 + sin (\frac{π y}{4})

= \frac{d y}{d y} (1 + sin (\frac{π y}{4})) + \frac{d}{d y} (1 + sin (\frac{π y}{4})) y

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

\frac{d}{d y} (1 + sin (\frac{π y}{4})) = \frac{π}{4} cos (\frac{π y}{4})

= 1 \cdot (1 + sin (\frac{π y}{4})) + \frac{π}{4} cos (\frac{π y}{4}) y

簡素化

1 \cdot (1 + sin (\frac{π y}{4})) + \frac{π}{4} cos (\frac{π y}{4}) y : 1 + sin (\frac{π y}{4}) + \frac{π y cos ( \frac{π y}{4} )}{4}

= 1 + sin (\frac{π y}{4}) + \frac{π y cos ( \frac{π y}{4} )}{4}