derivative ln(x+sqrt(x^2+1))

Lösung

ableitung von

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 \infty lim (\frac{x}{( ln ( x ) ) ^{3} + 2 x})

2 y \frac{d y}{d x} = \frac{x}{x ^{2} - 16}, y (5) = 2

\frac{d y}{d x} = 10 e^{x - y}

x^{^{''}} = x

\frac{\partial}{\partial y} (2 e^{y} x)