derivative of (x^2+32sqrt(x)/8)

解

\frac{d}{d x} (\frac{x ^{2} + 32 x}{8})

\frac{1}{8} (2 x + \frac{16}{x})

解答ステップ

\frac{d}{d x} (\frac{x ^{2} + 32 x}{8})

定数を除去:

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

= \frac{1}{8} \frac{d}{d x} (x^{2} + 32 x)

和/差の法則を適用:

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

= \frac{1}{8} (\frac{d}{d x} (x^{2}) + \frac{d}{d x} (32 x))

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

\frac{d}{d x} (32 x) = \frac{16}{x}

= \frac{1}{8} (2 x + \frac{16}{x})