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

Lösung

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

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

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{1}{x + 1 ( - x + 1 ) ^{\frac{3}{2}}}

= \frac{1}{( \frac{1 + x}{1 - x} ) ^{2} + 1} \cdot \frac{1}{x + 1 ( - x + 1 ) ^{\frac{3}{2}}}

Vereinfache

\frac{1}{( \frac{1 + x}{1 - x} ) ^{2} + 1} \cdot \frac{1}{x + 1 ( - x + 1 ) ^{\frac{3}{2}}} : \frac{1}{2 x + 1 ( - x + 1 ) ^{\frac{1}{2}}}

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

d er i v a t i v e x^{3} - 3

d er i v a t i v e (1 + cos^{2} (x))^{5}

n = 0 \sum \infty \frac{( e ^{n} )}{5}

\frac{d}{d x} (- 8 x^{3})

\int_{\frac{1}{7}}^{5} 6 x ln (7 x) d x