derivative of arctan(1+x^2)

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

x \to 5 lim (x 29 - x^{2})

\int sin^{6} (2 x) cos^{3} (2 x) d x

\frac{\partial}{\partial x} (x y - z^{2} + 17 x^{2} z)

t an g e n t y = - x^{2} + 4 x + 2, (3, 5)

\frac{\partial}{\partial x} (\frac{x}{y ^{3}})