derivative 7/3 x^3(4x^5-11)^3

解

導関数

\frac{7}{3} x^{3} (4 x^{5} - 11)^{3}

7 x^{2} (4 x^{5} - 11)^{2} (24 x^{5} - 11)

解答ステップ

\frac{d}{d x} (\frac{7}{3} x^{3} (4 x^{5} - 11)^{3})

定数を除去:

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

= \frac{7}{3} \frac{d}{d x} (x^{3} (4 x^{5} - 11)^{3})

積の法則を適用:

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

f = x^{3}, g = (4 x^{5} - 11)^{3}

= \frac{7}{3} (\frac{d}{d x} (x^{3}) (4 x^{5} - 11)^{3} + \frac{d}{d x} ((4 x^{5} - 11)^{3}) x^{3})

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

\frac{d}{d x} ((4 x^{5} - 11)^{3}) = 60 x^{4} (4 x^{5} - 11)^{2}

= \frac{7}{3} (3 x^{2} (4 x^{5} - 11)^{3} + 60 x^{4} (4 x^{5} - 11)^{2} x^{3})

簡素化

\frac{7}{3} (3 x^{2} (4 x^{5} - 11)^{3} + 60 x^{4} (4 x^{5} - 11)^{2} x^{3}) : 7 x^{2} (4 x^{5} - 11)^{2} (24 x^{5} - 11)

= 7 x^{2} (4 x^{5} - 11)^{2} (24 x^{5} - 11)