derivative of 5x^3sqrt(5x-2)

解

\frac{d}{d x} (5 x^{3} 5 x - 2)

\frac{5 ( 35 x ^{3} - 12 x ^{2} )}{2 5 x - 2}

解答ステップ

\frac{d}{d x} (5 x^{3} 5 x - 2)

定数を除去:

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

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

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = 5 x - 2

= 5 (\frac{d}{d x} (x^{3}) 5 x - 2 + \frac{d}{d x} (5 x - 2) x^{3})

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (5 x - 2) = \frac{5}{2 5 x - 2}

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

簡素化

5 (3 x^{2} 5 x - 2 + \frac{5}{2 5 x - 2} x^{3}) : \frac{5 ( 35 x ^{3} - 12 x ^{2} )}{2 5 x - 2}

= \frac{5 ( 35 x ^{3} - 12 x ^{2} )}{2 5 x - 2}