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

解

導関数

(3 x^{2} + x) (5 x^{3} + 1)

75 x^{4} + 20 x^{3} + 6 x + 1

解答ステップ

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

積の法則を適用:

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

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

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

\frac{d}{d x} (3 x^{2} + x) = 6 x + 1

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

= (6 x + 1) (5 x^{3} + 1) + 15 x^{2} (3 x^{2} + x)

簡素化

(6 x + 1) (5 x^{3} + 1) + 15 x^{2} (3 x^{2} + x) : 75 x^{4} + 20 x^{3} + 6 x + 1

= 75 x^{4} + 20 x^{3} + 6 x + 1