derivative of xsqrt(x^2-3x+2)

解

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

\frac{4 x ^{2} - 9 x + 4}{2 x ^{2} - 3 x + 2}

解答ステップ

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

積の法則を適用:

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

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

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

\frac{d x}{d x} = 1

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

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

簡素化

1 \cdot x^{2} - 3 x + 2 + \frac{2 x - 3}{2 x ^{2} - 3 x + 2} x : \frac{4 x ^{2} - 9 x + 4}{2 x ^{2} - 3 x + 2}

= \frac{4 x ^{2} - 9 x + 4}{2 x ^{2} - 3 x + 2}