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

Lösung

ableitung von

ln (x + 1 + x^{2})

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

x \to \infty lim (\frac{25 6 ^{\frac{x}{2}}}{4 ^{2 x}})

\int \frac{6}{x ^{2} + 4} d x

\int (2 x + 3)^{5} d x

\frac{d}{d x} (\frac{7}{x + 9})

\frac{d}{d x} (\frac{350}{x ^{2} + y ^{2}})