derivative of ln(x+sqrt(3+x^2))

Lösung

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

\frac{1}{3 + x ^{2}}

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{x + 3 + x ^{2}} \frac{d}{d x} (x + 3 + x^{2})

= \frac{1}{x + 3 + x ^{2}} \frac{d}{d x} (x + 3 + x^{2})

\frac{d}{d x} (x + 3 + x^{2}) = 1 + \frac{x}{3 + x ^{2}}

= \frac{1}{x + 3 + x ^{2}} (1 + \frac{x}{3 + x ^{2}})

Vereinfache

\frac{1}{x + 3 + x ^{2}} (1 + \frac{x}{3 + x ^{2}}) : \frac{1}{3 + x ^{2}}

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

x \to 0 lim (\frac{( x ^{3} + 3 x )}{x})

- 8 x^{2} y + y^{^{'}} = - 5 x^{2}

\int \frac{1}{3 - 4 sin ^{2} ( x )} d x

d er i v a t i v e f (x) = x^{2020}

\frac{d}{d x} ((x^{3} + 5 x)^{2} (5 x - 3)^{4})