derivative (sqrt(x)+2)(x^3-x)

解

導関数

(x + 2) (x^{3} - x)

\frac{7 x ^{2} x + 12 x ^{2} - 3 x}{2} - 2

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

\frac{1}{2 x} (x^{3} - x) + (3 x^{2} - 1) (x + 2) : \frac{7 x ^{2} x + 12 x ^{2} - 3 x}{2} - 2

= \frac{7 x ^{2} x + 12 x ^{2} - 3 x}{2} - 2