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Beliebt Rechnen >

derivative f(x)=(4x-3)(sqrt(x)+2)

Lösung

ableitung von

f (x) = (4 x - 3) (x + 2)

Lösung

\frac{12 x - 3}{2 x} + 8

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = 4 x - 3, g = x + 2

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

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

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

= 4 (x + 2) + \frac{1}{2 x} (4 x - 3)

Vereinfache

4 (x + 2) + \frac{1}{2 x} (4 x - 3) : \frac{12 x - 3}{2 x} + 8

= \frac{12 x - 3}{2 x} + 8

Graph

Beliebte Beispiele

derivative f(x)=x^2+10

d er i v a t i v e f (x) = x^{2} + 10

integral of sec^2(x)tan^{10}(x)

\int sec^{2} (x) tan^{10} (x) d x

taylor e^{(x+1)}

t a y l or e^{(x + 1)}

limit as x approaches 5 of 6

x \to 5 lim (6)

x^{''}+2x^'+4x=0

x^{^{''}} + 2 x^{^{'}} + 4 x = 0