derivative of (sqrt(x)/(9+x))

Lösung

\frac{d}{d x} (\frac{x}{9 + x})

\frac{9 - x}{2 x ( 9 + x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{9 + x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ) ( 9 + x ) - \frac{d}{d x} ( 9 + x ) x}{( 9 + x ) ^{2}}

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

\frac{d}{d x} (9 + x) = 1

= \frac{\frac{1}{2 x} ( 9 + x ) - 1 \cdot x}{( 9 + x ) ^{2}}

Vereinfache

\frac{\frac{1}{2 x} ( 9 + x ) - 1 \cdot x}{( 9 + x ) ^{2}} : \frac{9 - x}{2 x ( 9 + x ) ^{2}}

= \frac{9 - x}{2 x ( 9 + x ) ^{2}}

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

\int \frac{( e ^{2 x} )}{4 + e ^{4 x}} d x

\int l d l

x \to 1 lim (\frac{9}{x ^{3} - 1})

\int_{0}^{3} 2 π x (3 x - x^{2}) d x