derivative of x/(sqrt(x^2-1))

Lösung

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

- \frac{1}{( x ^{2} - 1 ) x ^{2} - 1}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d x}{d x} = 1

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

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

Vereinfache

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

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

\int ln (\frac{2}{x}) d x

d er i v a t i v e \frac{( 2 x ^{3} + 4 x ^{2} - 2 x + 3 )}{( x - 3 )}

\int x + 3 d x

\frac{\partial}{\partial x} (e^{x} y + 5 x y^{2} - x^{2})

n = 0 \sum \infty \frac{3}{n ^{4}}