(\partial)/(\partial x)(10sqrt(x))

解

\frac{\partial}{\partial x} (10 x)

\frac{5}{x}

解答ステップ

\frac{\partial}{\partial x} (10 x)

定数を除去:

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

= 10 \frac{\partial}{\partial x} (x)

累乗根の規則を適用する:

a = a^{\frac{1}{2}}

= 10 \frac{\partial}{\partial x} (x^{\frac{1}{2}})

乗の法則を適用:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 10 \cdot \frac{1}{2} x^{\frac{1}{2} - 1}

簡素化

10 \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{5}{x}

= \frac{5}{x}