derivative of sqrt(2500-x^2)

Lösung

\frac{d}{d x} (2500 - x^{2})

- \frac{x}{2500 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (2500 - x^{2})

Wende die Kettenregel an:

\frac{1}{2 2500 - x ^{2}} \frac{d}{d x} (2500 - x^{2})

= \frac{1}{2 2500 - x ^{2}} \frac{d}{d x} (2500 - x^{2})

\frac{d}{d x} (2500 - x^{2}) = - 2 x

= \frac{1}{2 2500 - x ^{2}} (- 2 x)

Vereinfache

\frac{1}{2 2500 - x ^{2}} (- 2 x) : - \frac{x}{2500 - x ^{2}}

= - \frac{x}{2500 - x ^{2}}

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