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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

n = 0 \sum \infty 10 (\frac{x}{3})^{n}

x \to + 2 lim (\frac{2 - x}{x ^{2} - 4})

\int \frac{( 5 x + 4 )}{5 x - 1} d x

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

d er i v a t i v e 16 t^{2}