derivative ln(1+x^2)

Lösung

ableitung von

ln (1 + x^{2})

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

Schritte zur Lösung

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

Vereinfache

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

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

\frac{\partial}{\partial y} (6 y^{2} e^{6 x y})

\frac{d}{d x} (x^{4} - 12 x^{3} + 48 x^{2} - 64 x)

\int \frac{x - 1}{( 2 x + 5 ) ( x - 8 )} d x

\int \frac{1}{t ^{2} 289 - t ^{2}} d t

\int_{- 7}^{7} \frac{1}{2} (49 - x^{2}) d x