derivative of 2xsqrt(36-x^2)

Lösung

\frac{d}{d x} (2 x 36 - x^{2})

\frac{2 ( - 2 x ^{2} + 36 )}{36 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (2 x 36 - x^{2})

Entferne die Konstante:

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

= 2 \frac{d}{d x} (x 36 - x^{2})

Wende die Produktregel an:

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

f = x, g = 36 - x^{2}

= 2 (\frac{d x}{d x} 36 - x^{2} + \frac{d}{d x} (36 - x^{2}) x)

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

\frac{d}{d x} (36 - x^{2}) = - \frac{x}{36 - x ^{2}}

= 2 (1 \cdot 36 - x^{2} + (- \frac{x}{36 - x ^{2}}) x)

Vereinfache

2 (1 \cdot 36 - x^{2} + (- \frac{x}{36 - x ^{2}}) x) : \frac{2 ( - 2 x ^{2} + 36 )}{36 - x ^{2}}

= \frac{2 ( - 2 x ^{2} + 36 )}{36 - x ^{2}}

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