derivative of (3x^5(6x^4+x)^4)

解

\frac{d}{d x} ((3 x^{5}) (6 x^{4} + x)^{4})

3 (5 x^{4} (6 x^{4} + x)^{4} + 4 (6 x^{4} + x)^{3} (24 x^{3} + 1) x^{5})

解答ステップ

\frac{d}{d x} ((3 x^{5}) (6 x^{4} + x)^{4})

定数を除去:

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

= 3 \frac{d}{d x} (x^{5} (6 x^{4} + x)^{4})

積の法則を適用:

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

f = x^{5}, g = (6 x^{4} + x)^{4}

= 3 (\frac{d}{d x} (x^{5}) (6 x^{4} + x)^{4} + \frac{d}{d x} ((6 x^{4} + x)^{4}) x^{5})

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

\frac{d}{d x} ((6 x^{4} + x)^{4}) = 4 (6 x^{4} + x)^{3} (24 x^{3} + 1)

= 3 (5 x^{4} (6 x^{4} + x)^{4} + 4 (6 x^{4} + x)^{3} (24 x^{3} + 1) x^{5})