derivative x^8(x-1)^7

解

導関数

x^{8} (x - 1)^{7}

8 x^{7} (x - 1)^{7} + 7 (x - 1)^{6} x^{8}

解答ステップ

\frac{d}{d x} (x^{8} (x - 1)^{7})

積の法則を適用:

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

f = x^{8}, g = (x - 1)^{7}

= \frac{d}{d x} (x^{8}) (x - 1)^{7} + \frac{d}{d x} ((x - 1)^{7}) x^{8}

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

\frac{d}{d x} ((x - 1)^{7}) = 7 (x - 1)^{6}

= 8 x^{7} (x - 1)^{7} + 7 (x - 1)^{6} x^{8}