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

Lösung

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

- \frac{x - 1}{16 x ( x + 1 ) ^{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} ( 8 x + 8 ) x}{( 8 x + 8 ) ^{2}}

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

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

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

Vereinfache

\frac{\frac{1}{2 x} ( 8 x + 8 ) - 8 x}{( 8 x + 8 ) ^{2}} : - \frac{x - 1}{16 x ( x + 1 ) ^{2}}

= - \frac{x - 1}{16 x ( x + 1 ) ^{2}}

x \to 9 lim (\frac{x + 8}{x + 9})

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