derivative 4x(2x-3)^7

Lösung

ableitung von

4 x (2 x - 3)^{7}

4 ((2 x - 3)^{7} + 14 x (2 x - 3)^{6})

Schritte zur Lösung

\frac{d}{d x} (4 x (2 x - 3)^{7})

Entferne die Konstante:

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

= 4 \frac{d}{d x} (x (2 x - 3)^{7})

Wende die Produktregel an:

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

f = x, g = (2 x - 3)^{7}

= 4 (\frac{d x}{d x} (2 x - 3)^{7} + \frac{d}{d x} ((2 x - 3)^{7}) x)

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

\frac{d}{d x} ((2 x - 3)^{7}) = 14 (2 x - 3)^{6}

= 4 (1 \cdot (2 x - 3)^{7} + 14 (2 x - 3)^{6} x)

Vereinfache

= 4 ((2 x - 3)^{7} + 14 x (2 x - 3)^{6})

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