derivative 7(x^2+3x)^6(2x+3)

Lösung

ableitung von

7 (x^{2} + 3 x)^{6} (2 x + 3)

7 (6 (x^{2} + 3 x)^{5} (2 x + 3)^{2} + 2 (x^{2} + 3 x)^{6})

Schritte zur Lösung

\frac{d}{d x} (7 (x^{2} + 3 x)^{6} (2 x + 3))

Entferne die Konstante:

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

= 7 \frac{d}{d x} ((x^{2} + 3 x)^{6} (2 x + 3))

Wende die Produktregel an:

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

f = (x^{2} + 3 x)^{6}, g = 2 x + 3

= 7 (\frac{d}{d x} ((x^{2} + 3 x)^{6}) (2 x + 3) + \frac{d}{d x} (2 x + 3) (x^{2} + 3 x)^{6})

\frac{d}{d x} ((x^{2} + 3 x)^{6}) = 6 (x^{2} + 3 x)^{5} (2 x + 3)

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

= 7 (6 (x^{2} + 3 x)^{5} (2 x + 3) (2 x + 3) + 2 (x^{2} + 3 x)^{6})

6 (x^{2} + 3 x)^{5} (2 x + 3) (2 x + 3) = 6 (x^{2} + 3 x)^{5} (2 x + 3)^{2}

= 7 (6 (x^{2} + 3 x)^{5} (2 x + 3)^{2} + 2 (x^{2} + 3 x)^{6})

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