(\partial)/(\partial x)((y+z)(arcsin(x)))

解

\frac{\partial}{\partial x} ((y + z) (arcsin (x)))

\frac{y + z}{1 - x ^{2}}

解答ステップ

\frac{\partial}{\partial x} ((y + z) (arcsin (x)))

y, z

を定数として扱う

定数を除去:

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

= (y + z) \frac{\partial}{\partial x} (arcsin (x))

共通の導関数を適用:

\frac{\partial}{\partial x} (arcsin (x)) = \frac{1}{1 - x ^{2}}

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

簡素化

(y + z) \frac{1}{1 - x ^{2}} : \frac{y + z}{1 - x ^{2}}

= \frac{y + z}{1 - x ^{2}}