derivative of (sqrt(5-2x)/(2x+1))

Lösung

\frac{d}{d x} (\frac{5 - 2 x}{2 x + 1})

\frac{2 x - 11}{( 2 x + 1 ) ^{2} 5 - 2 x}

Schritte zur Lösung

\frac{d}{d x} (\frac{5 - 2 x}{2 x + 1})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 5 - 2 x ) ( 2 x + 1 ) - \frac{d}{d x} ( 2 x + 1 ) 5 - 2 x}{( 2 x + 1 ) ^{2}}

\frac{d}{d x} (5 - 2 x) = - \frac{1}{5 - 2 x}

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

= \frac{( - \frac{1}{5 - 2 x} ) ( 2 x + 1 ) - 2 5 - 2 x}{( 2 x + 1 ) ^{2}}

Vereinfache

\frac{( - \frac{1}{5 - 2 x} ) ( 2 x + 1 ) - 2 5 - 2 x}{( 2 x + 1 ) ^{2}} : \frac{2 x - 11}{( 2 x + 1 ) ^{2} 5 - 2 x}

= \frac{2 x - 11}{( 2 x + 1 ) ^{2} 5 - 2 x}

x \to 0 + lim (x^{- 5} ln (x))

d er i v a t i v e 2 x^{3} - x

n = 2 \sum \infty \frac{1}{2 ^{n - 1}}

d er i v a t i v e 45 x^{8} - 12 x^{5}

\frac{d}{d x} (\frac{96}{x})