derivative x^7(x-10)^3

解

導関数

x^{7} (x - 10)^{3}

7 x^{6} (x - 10)^{3} + 3 (x - 10)^{2} x^{7}

解答ステップ

\frac{d}{d x} (x^{7} (x - 10)^{3})

積の法則を適用:

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

f = x^{7}, g = (x - 10)^{3}

= \frac{d}{d x} (x^{7}) (x - 10)^{3} + \frac{d}{d x} ((x - 10)^{3}) x^{7}

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

\frac{d}{d x} ((x - 10)^{3}) = 3 (x - 10)^{2}

= 7 x^{6} (x - 10)^{3} + 3 (x - 10)^{2} x^{7}