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

Lösung

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

\frac{4 x ( x ^{2} + 3 )}{( x - 1 ) ^{3} ( x + 1 ) ^{3}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (- 2 x^{2} - 2) = - 4 x

\frac{d}{d x} ((x - 1)^{2} (x + 1)^{2}) = 4 x^{3} - 4 x

= \frac{( - 4 x ) ( x - 1 ) ^{2} ( x + 1 ) ^{2} - ( 4 x ^{3} - 4 x ) ( - 2 x ^{2} - 2 )}{( ( x - 1 ) ^{2} ( x + 1 ) ^{2} ) ^{2}}

Vereinfache

\frac{( - 4 x ) ( x - 1 ) ^{2} ( x + 1 ) ^{2} - ( 4 x ^{3} - 4 x ) ( - 2 x ^{2} - 2 )}{( ( x - 1 ) ^{2} ( x + 1 ) ^{2} ) ^{2}} : \frac{4 x ( x ^{2} + 3 )}{( x - 1 ) ^{3} ( x + 1 ) ^{3}}

= \frac{4 x ( x ^{2} + 3 )}{( x - 1 ) ^{3} ( x + 1 ) ^{3}}

a re a x = (y - 1)^{2}, x = 13 - y^{2}

\int \frac{2 x}{e ^{2 x}} d x

x \to 2 + lim (g (x))

\frac{d}{d x} (arctan (8^{x}))

\int - 0.006 t^{2} + 0.2 t d t