(\partial)/(\partial x)((sin(x+y))/(y^2))

解

\frac{\partial}{\partial x} (\frac{sin ( x + y )}{y ^{2}})

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

解答ステップ

\frac{\partial}{\partial x} (\frac{sin ( x + y )}{y ^{2}})

y

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{y ^{2}} \frac{\partial}{\partial x} (sin (x + y))

連鎖法則を適用:

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

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

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

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

簡素化

\frac{1}{y ^{2}} cos (x + y) \cdot 1 : \frac{cos ( x + y )}{y ^{2}}

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