derivative of arctan(x^2+1)

Lösung

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

\frac{2 x}{x ^{4} + 2 x ^{2} + 2}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{( x ^{2} + 1 ) ^{2} + 1} \cdot 2 x : \frac{2 x}{x ^{4} + 2 x ^{2} + 2}

= \frac{2 x}{x ^{4} + 2 x ^{2} + 2}

n = 1 \sum \infty \frac{50}{5 ^{n}}

d er i v a t i v e e^{l n (s e c (2 x))}

\frac{d}{d x} (\frac{sin ( 2 x )}{2})

y^{^{''}} - 5 y^{^{'}} + 6 y = x e^{x}

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