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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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})

Vereinfache

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

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

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