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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

d er i v a t i v e y = \frac{x + 2}{x - 2}

d y = (9 x + 4 y + 1)^{2} d x

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