derivative (sqrt(x)-7)/(sqrt(x)+7)

Lösung

ableitung von

\frac{x - 7}{x + 7}

\frac{7}{x ( x + 7 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x - 7}{x + 7})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x - 7 ) ( x + 7 ) - \frac{d}{d x} ( x + 7 ) ( x - 7 )}{( x + 7 ) ^{2}}

\frac{d}{d x} (x - 7) = \frac{1}{2 x}

\frac{d}{d x} (x + 7) = \frac{1}{2 x}

= \frac{\frac{1}{2 x} ( x + 7 ) - \frac{1}{2 x} ( x - 7 )}{( x + 7 ) ^{2}}

Vereinfache

\frac{\frac{1}{2 x} ( x + 7 ) - \frac{1}{2 x} ( x - 7 )}{( x + 7 ) ^{2}} : \frac{7}{x ( x + 7 ) ^{2}}

= \frac{7}{x ( x + 7 ) ^{2}}

x \to - 1 lim (3 - x^{2})

\int 2 sin (x) + 2 x^{2} + 5 x + 1 d x

\frac{d}{d x} (\frac{2 x - 3}{x ^{2}})

\int \frac{81 + x ^{2}}{x} d x

x \to \infty lim (3 x^{3} + 3 x^{2} - x)