derivative of xsqrt(3x-2)

Lösung

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

\frac{9 x - 4}{2 3 x - 2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = 3 x - 2

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

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

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

= 1 \cdot 3 x - 2 + \frac{3}{2 3 x - 2} x

Vereinfache

1 \cdot 3 x - 2 + \frac{3}{2 3 x - 2} x : \frac{9 x - 4}{2 3 x - 2}

= \frac{9 x - 4}{2 3 x - 2}