derivative of 12x(x^2+10^5)

Lösung

\frac{d}{d x} (12 x (x^{2} + 10)^{5})

12 ((x^{2} + 10)^{5} + 10 x^{2} (x^{2} + 10)^{4})

Schritte zur Lösung

\frac{d}{d x} (12 x (x^{2} + 10)^{5})

Entferne die Konstante:

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

= 12 \frac{d}{d x} (x (x^{2} + 10)^{5})

Wende die Produktregel an:

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

f = x, g = (x^{2} + 10)^{5}

= 12 (\frac{d x}{d x} (x^{2} + 10)^{5} + \frac{d}{d x} ((x^{2} + 10)^{5}) x)

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

\frac{d}{d x} ((x^{2} + 10)^{5}) = 10 x (x^{2} + 10)^{4}

= 12 (1 \cdot (x^{2} + 10)^{5} + 10 x (x^{2} + 10)^{4} x)

Vereinfache

12 (1 \cdot (x^{2} + 10)^{5} + 10 x (x^{2} + 10)^{4} x) : 12 ((x^{2} + 10)^{5} + 10 x^{2} (x^{2} + 10)^{4})

= 12 ((x^{2} + 10)^{5} + 10 x^{2} (x^{2} + 10)^{4})

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