derivative of log_{e}(x^2+1)

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

lo g_{e} (x^{2} + 1) : ln (x^{2} + 1)

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int \frac{e ^{3 x}}{1 - e ^{6 x}} d x

x \to \infty lim (\frac{5 - 2 x ^{\frac{3}{2}}}{3 x - 4})

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

d er i v a t i v e arctan (\frac{7}{x ^{2}})

d er i v a t i v e (3 x + 4) x^{2}