derivative of 500(1+x/(1200)^{120})

解

\frac{d}{d x} (500 (1 + \frac{x}{1200})^{120})

50 (\frac{x}{1200} + 1)^{119}

解答ステップ

\frac{d}{d x} (500 (1 + \frac{x}{1200})^{120})

定数を除去:

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

= 500 \frac{d}{d x} ((1 + \frac{x}{1200})^{120})

連鎖法則を適用:

120 (1 + \frac{x}{1200})^{119} \frac{d}{d x} (1 + \frac{x}{1200})

= 120 (1 + \frac{x}{1200})^{119} \frac{d}{d x} (1 + \frac{x}{1200})

\frac{d}{d x} (1 + \frac{x}{1200}) = \frac{1}{1200}

= 500 \cdot 120 (1 + \frac{x}{1200})^{119} \frac{1}{1200}

簡素化

500 \cdot 120 (1 + \frac{x}{1200})^{119} \frac{1}{1200} : 50 (\frac{x}{1200} + 1)^{119}

= 50 (\frac{x}{1200} + 1)^{119}