derivative of (5(x^4-(10)/x))

解

\frac{d}{d x} ((5) (x^{4} - \frac{10}{x}))

5 (4 x^{3} + \frac{10}{x ^{2}})

解答ステップ

\frac{d}{d x} ((5) (x^{4} - \frac{10}{x}))

定数を除去:

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

= 5 \frac{d}{d x} (x^{4} - \frac{10}{x})

和/差の法則を適用:

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

= 5 (\frac{d}{d x} (x^{4}) - \frac{d}{d x} (\frac{10}{x}))

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (\frac{10}{x}) = - \frac{10}{x ^{2}}

= 5 (4 x^{3} - (- \frac{10}{x ^{2}}))

簡素化

= 5 (4 x^{3} + \frac{10}{x ^{2}})