derivative of sqrt(x)(x-1^2)

解

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

\frac{5 x ^{2} - 6 x + 1}{2 x}

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

\frac{1}{2 x} (x - 1)^{2} + 2 (x - 1) x : \frac{5 x ^{2} - 6 x + 1}{2 x}

= \frac{5 x ^{2} - 6 x + 1}{2 x}