derivative f(x)=((x^2-3x))/2

解

導関数

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

x - \frac{3}{2}

解答ステップ

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

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (3 x) = 3

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

簡素化

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

= x - \frac{3}{2}