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

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

\frac{x - 1}{x + 1} : \frac{x - 1}{x + 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial x} (\frac{1}{2} ln (x + y))

y^{^{''}} + k^{2} y = 0

\int sec^{4} (5 x) tan^{6} (5 x) d x

d er i v a t i v e \frac{ln ( 1 + x )}{1 - x}

x^{2} - y^{2} + x y \frac{d y}{d x} = 0