derivative y=ln(x+sqrt(x^2-1))

Lösung

ableitung von

y = ln (x + x^{2} - 1)

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

x \to 0 + lim (ln (\frac{1}{x}))

x \to 1 lim (7 ∣ x + 1 ∣ - 4)

d er i v a t i v e y = (x - 1) (x^{2} + x + 1)

\frac{d y}{d x} = \frac{2 x}{y + 1}

\int_{1}^{1000} \frac{25}{x ^{3}} d x