derivative f(x)=(5x^3+2)(3x^3+2)

解

導関数

f (x) = (5 x^{3} + 2) (3 x^{3} + 2)

90 x^{5} + 48 x^{2}

解答ステップ

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

積の法則を適用:

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

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

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

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

\frac{d}{d x} (3 x^{3} + 2) = 9 x^{2}

= 15 x^{2} (3 x^{3} + 2) + 9 x^{2} (5 x^{3} + 2)

簡素化

15 x^{2} (3 x^{3} + 2) + 9 x^{2} (5 x^{3} + 2) : 90 x^{5} + 48 x^{2}

= 90 x^{5} + 48 x^{2}