derivative of (sqrt(x)-8/(sqrt(x)+8))

Lösung

\frac{d}{d x} (\frac{x - 8}{x + 8})

\frac{8}{x ( x + 8 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x - 8}{x + 8})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x - 8 ) ( x + 8 ) - \frac{d}{d x} ( x + 8 ) ( x - 8 )}{( x + 8 ) ^{2}}

\frac{d}{d x} (x - 8) = \frac{1}{2 x}

\frac{d}{d x} (x + 8) = \frac{1}{2 x}

= \frac{\frac{1}{2 x} ( x + 8 ) - \frac{1}{2 x} ( x - 8 )}{( x + 8 ) ^{2}}

Vereinfache

\frac{\frac{1}{2 x} ( x + 8 ) - \frac{1}{2 x} ( x - 8 )}{( x + 8 ) ^{2}} : \frac{8}{x ( x + 8 ) ^{2}}

= \frac{8}{x ( x + 8 ) ^{2}}

x \to 4 lim ((x - 4)^{5} - 5)

x \to 3 lim (- 1)

\frac{d}{d x} (\frac{3}{4} x^{\frac{4}{3}} - \frac{3}{8} x^{\frac{2}{3}} + 5)

f (x) = 2 - x

d er i v a t i v e f (x) = \frac{1}{2 x ^{2}}