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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

n \to \infty lim (n^{- 2} e^{3 n})

s l o p e (- 2, - 4), (2, 2)

s l o p e 2 x^{2} + 4 x - 7

\int \frac{1}{4 u ^{2} + 9} d u

x \to \frac{π}{3} lim (\frac{1}{cot ( x )})