derivative arctan((1+x)/(1-x))

Lösung

ableitung von

arctan (\frac{1 + x}{1 - x})

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

Schritte zur Lösung

\frac{d}{d x} (arctan (\frac{1 + x}{1 - x}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

2 + \frac{d y}{d x} = 2 x + y

\frac{d}{d x} (\frac{in x}{x})

x \to 8 lim (e^{\frac{3}{( x - 8 )}})

\int \frac{2}{x - 2} d x

\int arccsc (\frac{x}{2}) d x