derivative f(x)=(x^2-3x)ln(x^2-3x)

Lösung

ableitung von

f (x) = (x^{2} - 3 x) ln (x^{2} - 3 x)

ln (x^{2} - 3 x) (2 x - 3) + 2 x - 3

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

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

= ln (x^{2} - 3 x) (2 x - 3) + 2 x - 3

z = - 3 - 3 i

t an g e n t y = x^{2} + 1

d er i v a t i v e f (x) = - 2 x + 2

d er i v a t i v e ln (3) x^{2}

s l o p e x = - 4