derivative of 1/2 (x^3+1)

解

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

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

解答ステップ

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

定数を除去:

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

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

和/差の法則を適用:

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

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

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

\frac{d}{d x} (1) = 0

= \frac{1}{2} (3 x^{2} + 0)

簡素化

\frac{1}{2} (3 x^{2} + 0) : \frac{3 x ^{2}}{2}

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