derivative of (5x^{1/2})

解

\frac{d}{d x} ((5 x)^{\frac{1}{2}})

\frac{5 ^{\frac{1}{2}}}{2 x ^{\frac{1}{2}}}

解答ステップ

\frac{d}{d x} ((5 x)^{\frac{1}{2}})

簡素化

(5 x)^{\frac{1}{2}} : 5^{\frac{1}{2}} x^{\frac{1}{2}}

= \frac{d}{d x} (5^{\frac{1}{2}} x^{\frac{1}{2}})

定数を除去:

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

= 5^{\frac{1}{2}} \frac{d}{d x} (x^{\frac{1}{2}})

乗の法則を適用:

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

= 5^{\frac{1}{2}} \cdot \frac{1}{2} x^{\frac{1}{2} - 1}

簡素化

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

= \frac{5 ^{\frac{1}{2}}}{2 x ^{\frac{1}{2}}}