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

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

分数を乗じる:

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

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