derivative cos(x/(sqrt(x+2)))

解

導関数

cos (\frac{x}{x + 2})

- \frac{sin ( \frac{x}{x + 2} ) ( x + 4 )}{2 ( x + 2 ) x + 2}

解答ステップ

\frac{d}{d x} (cos (\frac{x}{x + 2}))

連鎖法則を適用:

- sin (\frac{x}{x + 2}) \frac{d}{d x} (\frac{x}{x + 2})

= - sin (\frac{x}{x + 2}) \frac{d}{d x} (\frac{x}{x + 2})

\frac{d}{d x} (\frac{x}{x + 2}) = \frac{x + 4}{2 ( x + 2 ) x + 2}

= - sin (\frac{x}{x + 2}) \frac{x + 4}{2 ( x + 2 ) x + 2}

分数を乗じる:

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

= - \frac{sin ( \frac{x}{x + 2} ) ( x + 4 )}{2 ( x + 2 ) x + 2}