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

解

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

x

解答ステップ

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

y

を定数として扱う

定数を除去:

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

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

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (y^{2}) = 0

= \frac{1}{2} (2 x + 0)

簡素化

\frac{1}{2} (2 x + 0) : x

= x