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Beliebt Rechnen >

derivative y=3x(a^2-x^2)

Lösung

ableitung von

y = 3 x (a^{2} - x^{2})

Lösung

3 (a^{2} - 3 x^{2})

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = a^{2} - x^{2}

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

\frac{d x}{d x} = 1

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

= 3 (1 \cdot (a^{2} - x^{2}) + (- 2 x) x)

Vereinfache

3 (1 \cdot (a^{2} - x^{2}) + (- 2 x) x) : 3 (a^{2} - 3 x^{2})

= 3 (a^{2} - 3 x^{2})

Graph

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