derivative of (sqrt(x)-1/(sqrt(x)+3))

Lösung

\frac{d}{d x} (\frac{x - 1}{x + 3})

\frac{2}{x ( x + 3 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x - 1}{x + 3})

Wende die Quotientenregel an:

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

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

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

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

= \frac{\frac{1}{2 x} ( x + 3 ) - \frac{1}{2 x} ( x - 1 )}{( x + 3 ) ^{2}}

Vereinfache

\frac{\frac{1}{2 x} ( x + 3 ) - \frac{1}{2 x} ( x - 1 )}{( x + 3 ) ^{2}} : \frac{2}{x ( x + 3 ) ^{2}}

= \frac{2}{x ( x + 3 ) ^{2}}

d er i v a t i v e \frac{3 x}{x ^{2} - 6}

\int x sin (5 b x) d x

n = 1 \sum \infty \frac{x ^{n}}{5 ^{n}}

y^{^{'}} - \frac{2}{x} y = \frac{y ^{5}}{x ^{2}}, y (1) = 1

\frac{d}{d x} (2 x^{2} + x - 6)