derivative of (5x-1^3(x^2+1)^5)

解

\frac{d}{d x} ((5 x - 1)^{3} (x^{2} + 1)^{5})

15 (5 x - 1)^{2} (x^{2} + 1)^{5} + 10 x (x^{2} + 1)^{4} (5 x - 1)^{3}

解答ステップ

\frac{d}{d x} ((5 x - 1)^{3} (x^{2} + 1)^{5})

積の法則を適用:

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

f = (5 x - 1)^{3}, g = (x^{2} + 1)^{5}

= \frac{d}{d x} ((5 x - 1)^{3}) (x^{2} + 1)^{5} + \frac{d}{d x} ((x^{2} + 1)^{5}) (5 x - 1)^{3}

\frac{d}{d x} ((5 x - 1)^{3}) = 15 (5 x - 1)^{2}

\frac{d}{d x} ((x^{2} + 1)^{5}) = 10 x (x^{2} + 1)^{4}

= 15 (5 x - 1)^{2} (x^{2} + 1)^{5} + 10 x (x^{2} + 1)^{4} (5 x - 1)^{3}