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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

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

Vereinfache

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

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

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

y^{^{''}} - y^{^{'}} - 2 y = 0, y (0) = 0, y (\frac{π}{2}) = 1

d er i v a t i v e f (x) = 4 x^{2} - 1

t an g e n t y = (1 + 5 x)^{12}, (0, 1)

\frac{d x}{d t} = sin (x)