derivative y=(x^2+7x-2)/(x-2)

Lösung

ableitung von

y = \frac{x ^{2} + 7 x - 2}{x - 2}

\frac{x ^{2} - 4 x - 12}{( x - 2 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} + 7 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} + 7 x - 2 ) ( x - 2 ) - \frac{d}{d x} ( x - 2 ) ( x ^{2} + 7 x - 2 )}{( x - 2 ) ^{2}}

\frac{d}{d x} (x^{2} + 7 x - 2) = 2 x + 7

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

= \frac{( 2 x + 7 ) ( x - 2 ) - 1 \cdot ( x ^{2} + 7 x - 2 )}{( x - 2 ) ^{2}}

Vereinfache

\frac{( 2 x + 7 ) ( x - 2 ) - 1 \cdot ( x ^{2} + 7 x - 2 )}{( x - 2 ) ^{2}} : \frac{x ^{2} - 4 x - 12}{( x - 2 ) ^{2}}

= \frac{x ^{2} - 4 x - 12}{( x - 2 ) ^{2}}

\frac{d x}{d t} = 4 (x^{2} + 1), x (\frac{π}{4}) = 1

\int tan^{4} (2 x) d x

t^{5} y^{4} - t^{3} y^{^{'}} + 6 y = 0

y^{^{'}} = \frac{3 ( e ^{x} + 1 )}{2 y}

s im pl i f y \frac{d}{dd} (\frac{a x + b}{c x + d})