derivative of sin(x/(1+y))

解

\frac{d}{d x} (sin (\frac{x}{1 + y}))

\frac{cos ( \frac{x}{1 + y} ) ( 1 + y - x \frac{d y}{d x} )}{( 1 + y ) ^{2}}

解答ステップ

\frac{d}{d x} (sin (\frac{x}{1 + y}))

連鎖法則を適用:

cos (\frac{x}{1 + y}) \frac{d}{d x} (\frac{x}{1 + y})

= cos (\frac{x}{1 + y}) \frac{d}{d x} (\frac{x}{1 + y})

\frac{d}{d x} (\frac{x}{1 + y}) = \frac{1 + y - x \frac{d y}{d x}}{( 1 + y ) ^{2}}

= cos (\frac{x}{1 + y}) \frac{1 + y - x \frac{d y}{d x}}{( 1 + y ) ^{2}}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{cos ( \frac{x}{1 + y} ) ( 1 + y - x \frac{d y}{d x} )}{( 1 + y ) ^{2}}