(\partial)/(\partial x)(sin(x/(1+y)))

解

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

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

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

\frac{\partial}{\partial x} (\frac{x}{1 + y}) = \frac{1}{1 + y}

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

簡素化

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

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