derivative 75(1-t/(24))^2

解

導関数

75 (1 - \frac{t}{24})^{2}

- \frac{25}{4} (1 - \frac{t}{24})

解答ステップ

\frac{d}{d t} (75 (1 - \frac{t}{24})^{2})

定数を除去:

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

= 75 \frac{d}{d t} ((1 - \frac{t}{24})^{2})

連鎖法則を適用:

2 (1 - \frac{t}{24}) \frac{d}{d t} (1 - \frac{t}{24})

= 2 (1 - \frac{t}{24}) \frac{d}{d t} (1 - \frac{t}{24})

\frac{d}{d t} (1 - \frac{t}{24}) = - \frac{1}{24}

= 75 \cdot 2 (1 - \frac{t}{24}) (- \frac{1}{24})

簡素化

75 \cdot 2 (1 - \frac{t}{24}) (- \frac{1}{24}) : - \frac{25}{4} (1 - \frac{t}{24})

= - \frac{25}{4} (1 - \frac{t}{24})