derivative of (x^2+40x/5)

解

\frac{d}{d x} (\frac{x ^{2} + 40 x}{5})

\frac{1}{5} (2 x + 40)

解答ステップ

\frac{d}{d x} (\frac{x ^{2} + 40 x}{5})

定数を除去:

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

= \frac{1}{5} \frac{d}{d x} (x^{2} + 40 x)

和/差の法則を適用:

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

= \frac{1}{5} (\frac{d}{d x} (x^{2}) + \frac{d}{d x} (40 x))

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

\frac{d}{d x} (40 x) = 40

= \frac{1}{5} (2 x + 40)