derivative of (5x^3-2x^2(6x^3))

解

\frac{d}{d x} ((5 x^{3} - 2 x^{2}) (6 x^{3}))

6 (30 x^{5} - 10 x^{4})

解答ステップ

\frac{d}{d x} ((5 x^{3} - 2 x^{2}) (6 x^{3}))

定数を除去:

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

= 6 \frac{d}{d x} ((5 x^{3} - 2 x^{2}) x^{3})

積の法則を適用:

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

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

= 6 (\frac{d}{d x} (5 x^{3} - 2 x^{2}) x^{3} + \frac{d}{d x} (x^{3}) (5 x^{3} - 2 x^{2}))

\frac{d}{d x} (5 x^{3} - 2 x^{2}) = 15 x^{2} - 4 x

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

= 6 ((15 x^{2} - 4 x) x^{3} + 3 x^{2} (5 x^{3} - 2 x^{2}))

拡張

(15 x^{2} - 4 x) x^{3} + 3 x^{2} (5 x^{3} - 2 x^{2}) : 30 x^{5} - 10 x^{4}

= 6 (30 x^{5} - 10 x^{4})