derivative xsqrt(x^2-1)

Lösung

ableitung von

x x^{2} - 1

\frac{2 x ^{2} - 1}{x ^{2} - 1}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = x^{2} - 1

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

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

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

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

Vereinfache

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

= \frac{2 x ^{2} - 1}{x ^{2} - 1}

x \to 4 - lim (\frac{3 x}{x - 4})

\int 2 x (x^{2} + 7)^{5} d x

s l o p e (0, 5), (3, - 5)

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

\int_{1}^{5} 10