derivative of (2x^2-3x/(x-2))

Lösung

\frac{d}{d x} (\frac{2 x ^{2} - 3 x}{x - 2})

\frac{2 x ^{2} - 8 x + 6}{( x - 2 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x ^{2} - 3 x}{x - 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} - 3 x ) ( x - 2 ) - \frac{d}{d x} ( x - 2 ) ( 2 x ^{2} - 3 x )}{( x - 2 ) ^{2}}

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

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

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

Vereinfache

\frac{( 4 x - 3 ) ( x - 2 ) - 1 \cdot ( 2 x ^{2} - 3 x )}{( x - 2 ) ^{2}} : \frac{2 x ^{2} - 8 x + 6}{( x - 2 ) ^{2}}

= \frac{2 x ^{2} - 8 x + 6}{( x - 2 ) ^{2}}

\frac{\partial}{\partial x} (6 y + 1)

x \to 0 - lim (sin (\frac{π}{x}))

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

d er i v a t i v e f (x) = 2 x - 5 x^{\frac{3}{4}}

\int_{3}^{\infty} \frac{6}{x ^{2} - x} d x