derivative f(x)=3sqrt(25-x^2)

Lösung

ableitung von

f (x) = 3 25 - x^{2}

- \frac{3 x}{25 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (3 25 - x^{2})

Entferne die Konstante:

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

= 3 \frac{d}{d x} (25 - x^{2})

Wende die Kettenregel an:

\frac{1}{2 25 - x ^{2}} \frac{d}{d x} (25 - x^{2})

= \frac{1}{2 25 - x ^{2}} \frac{d}{d x} (25 - x^{2})

\frac{d}{d x} (25 - x^{2}) = - 2 x

= 3 \cdot \frac{1}{2 25 - x ^{2}} (- 2 x)

Vereinfache

3 \cdot \frac{1}{2 25 - x ^{2}} (- 2 x) : - \frac{3 x}{25 - x ^{2}}

= - \frac{3 x}{25 - x ^{2}}

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