derivative of x^5(3+8x^7)

解

\frac{d}{d x} (x^{5} (3 + 8 x)^{7})

5 x^{4} (3 + 8 x)^{7} + 56 (3 + 8 x)^{6} x^{5}

解答ステップ

\frac{d}{d x} (x^{5} (3 + 8 x)^{7})

積の法則を適用:

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

f = x^{5}, g = (3 + 8 x)^{7}

= \frac{d}{d x} (x^{5}) (3 + 8 x)^{7} + \frac{d}{d x} ((3 + 8 x)^{7}) x^{5}

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

\frac{d}{d x} ((3 + 8 x)^{7}) = 56 (3 + 8 x)^{6}

= 5 x^{4} (3 + 8 x)^{7} + 56 (3 + 8 x)^{6} x^{5}