derivative of xsqrt(x^2-3x+2)

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = x^{2} - 3 x + 2

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

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

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

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

Vereinfache

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

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

\int 9 x - 5 d x

x \to - 1 lim (6 x + 5)

\frac{d}{d x} (arccos (\frac{x}{1 - x ^{2}}))

f (x) = cos^{6} (x)

x \to 4 lim (x (x + 5) (x + 6))