derivative of (x-11/(sqrt(x)-\sqrt{11)})

Lösung

\frac{d}{d x} (\frac{x - 11}{x - 11})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x - 11}{x - 11})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x - 11 ) ( x - 11 ) - \frac{d}{d x} ( x - 11 ) ( x - 11 )}{( x - 11 ) ^{2}}

\frac{d}{d x} (x - 11) = 1

\frac{d}{d x} (x - 11) = \frac{1}{2 x}

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

Vereinfache

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

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

\int \frac{1}{1 + 2 e ^{x} - e ^{- x}} d x

d er i v a t i v e (3 x + 5)^{7}

y^{^{'}} - \frac{y}{( 100 + 4 t )} = 150

s l o p e in t erce pt (- 2, - 5), (- 4, 4)

x \to 4 lim (x^{4} e^{- x^{3}})