derivative y=(Ax^2)/(x^2-1)

Lösung

ableitung von

y = \frac{A x ^{2}}{x ^{2} - 1}

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= A \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}}

= A \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) = 2 x

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

Vereinfache

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

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

\frac{d}{d x} (4 x^{3} + 5 x^{2} + x + 6)

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

\int \frac{1}{x ^{2} 2 + 9 x ^{2}} d x

\frac{\partial}{\partial y} ((x^{2} + y^{2}) ln (x^{2} + y^{2}))

d er i v a t i v e 5 t^{- \frac{3}{5}}