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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Vereinfache

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

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

x \to \infty lim (\frac{x ^{2} - 9}{2 x - 6})

y^{^{''}} - 8 y^{^{'}} + 16 y = e^{4 x}

\frac{d}{d x} (4 x^{2} + 6 x)

\frac{\partial}{\partial s} (s^{6} + t^{6})

\frac{df}{d x} + 2 f = f x^{3}