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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

d er i v a t i v e \frac{7 + 2 x}{5 - 8 x}

\frac{\partial}{\partial x} (\frac{1}{tan ( x y )})

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

\frac{\partial}{\partial x} (e^{- 2 x} \cdot cos (2 y))

\int \frac{5 x - 3}{x ^{2} - 1} d x