derivative y=(sqrt(x)-5)/(sqrt(x)+5)

Lösung

ableitung von

y = \frac{x - 5}{x + 5}

\frac{5}{x ( x + 5 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x - 5}{x + 5})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x - 5 ) ( x + 5 ) - \frac{d}{d x} ( x + 5 ) ( x - 5 )}{( x + 5 ) ^{2}}

\frac{d}{d x} (x - 5) = \frac{1}{2 x}

\frac{d}{d x} (x + 5) = \frac{1}{2 x}

= \frac{\frac{1}{2 x} ( x + 5 ) - \frac{1}{2 x} ( x - 5 )}{( x + 5 ) ^{2}}

Vereinfache

\frac{\frac{1}{2 x} ( x + 5 ) - \frac{1}{2 x} ( x - 5 )}{( x + 5 ) ^{2}} : \frac{5}{x ( x + 5 ) ^{2}}

= \frac{5}{x ( x + 5 ) ^{2}}

\frac{d}{d x} ((2 x + 1)^{2} 3 (2 x + 1) + 10)

in v erse l a pl a ce \frac{1}{s ^{2} - s + 1}

n = 0 \sum \infty 7 (\frac{2}{3})^{n}

\int (x^{3} + 1)^{2} x d x

x \to 3 lim (\frac{x + 3}{x + 2})