derivative of 1000(1-x/(500)^2)

Lösung

\frac{d}{d x} (1000 (1 - \frac{x}{500})^{2})

- 4 (1 - \frac{x}{500})

Schritte zur Lösung

\frac{d}{d x} (1000 (1 - \frac{x}{500})^{2})

Entferne die Konstante:

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

= 1000 \frac{d}{d x} ((1 - \frac{x}{500})^{2})

Wende die Kettenregel an:

2 (1 - \frac{x}{500}) \frac{d}{d x} (1 - \frac{x}{500})

= 2 (1 - \frac{x}{500}) \frac{d}{d x} (1 - \frac{x}{500})

\frac{d}{d x} (1 - \frac{x}{500}) = - \frac{1}{500}

= 1000 \cdot 2 (1 - \frac{x}{500}) (- \frac{1}{500})

Vereinfache

1000 \cdot 2 (1 - \frac{x}{500}) (- \frac{1}{500}) : - 4 (1 - \frac{x}{500})

= - 4 (1 - \frac{x}{500})

\frac{d y}{d x} = 4 + 9 x + 32 y + 72 x y

\int_{0}^{t} e^{s} sin (t - s) d s

d er i v a t i v e f (s) = - \frac{12}{s ^{5}}

\frac{d}{d x} (x ln (x^{15}))

d er i v a t i v e \frac{1}{27} (9 x^{2} + 6)^{\frac{3}{2}}