derivative of 1000(1-x/(60)^2)

Lösung

\frac{d}{d x} (1000 (1 - \frac{x}{60})^{2})

- \frac{100}{3} (1 - \frac{x}{60})

Schritte zur Lösung

\frac{d}{d x} (1000 (1 - \frac{x}{60})^{2})

Entferne die Konstante:

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

= 1000 \frac{d}{d x} ((1 - \frac{x}{60})^{2})

Wende die Kettenregel an:

2 (1 - \frac{x}{60}) \frac{d}{d x} (1 - \frac{x}{60})

= 2 (1 - \frac{x}{60}) \frac{d}{d x} (1 - \frac{x}{60})

\frac{d}{d x} (1 - \frac{x}{60}) = - \frac{1}{60}

= 1000 \cdot 2 (1 - \frac{x}{60}) (- \frac{1}{60})

Vereinfache

1000 \cdot 2 (1 - \frac{x}{60}) (- \frac{1}{60}) : - \frac{100}{3} (1 - \frac{x}{60})

= - \frac{100}{3} (1 - \frac{x}{60})

y^{^{'}} = 1 + \frac{y}{x}

y^{^{''}} - y = - x

\int e^{x^{- 1}} d x

t an g e n t y = x^{3} - 7 x^{2} + 16 x + 7, at

\frac{d}{d x} (\frac{6 x}{7 - tan ( x )})