derivative f(x)=(5x-5)(sqrt(x)+3)

Lösung

ableitung von

f (x) = (5 x - 5) (x + 3)

\frac{15 x - 5}{2 x} + 15

Schritte zur Lösung

\frac{d}{d x} ((5 x - 5) (x + 3))

Wende die Produktregel an:

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

f = 5 x - 5, g = x + 3

= \frac{d}{d x} (5 x - 5) (x + 3) + \frac{d}{d x} (x + 3) (5 x - 5)

\frac{d}{d x} (5 x - 5) = 5

\frac{d}{d x} (x + 3) = \frac{1}{2 x}

= 5 (x + 3) + \frac{1}{2 x} (5 x - 5)

Vereinfache

5 (x + 3) + \frac{1}{2 x} (5 x - 5) : \frac{15 x - 5}{2 x} + 15

= \frac{15 x - 5}{2 x} + 15

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