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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

Vereinfache

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

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

\int_{0}^{5} \frac{1}{1 + x ^{2}} d x

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

\int (2 x - 3 x - x^{4}) d x

y^{^{''}} + y^{^{'}} = sec (x) tan (x)

d er i v a t i v e f (x) = \frac{8 x}{8 + x}