derivative f(x)=sqrt(x)(x^3-x)

解

導関数

f (x) = x (x^{3} - x)

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

解答ステップ

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

積の法則を適用:

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

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

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

\frac{d}{d x} (x) = \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

簡素化

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

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