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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

a re a x^{2} - 2 x + 3, x = - 2, x = 1

\frac{d}{d x} ((2 x^{2} - 6)^{- 10})

y^{^{''}} - 8 y^{^{'}} + 16 y = t - 2 e^{4 t}

\int (x^{3} - 1)^{2} d x

\frac{d y}{d x} = cos (x) \cdot e^{y + s i n (x)}