derivative (x^2-3x+2)/(-x^2-4x-4)

Lösung

ableitung von

\frac{x ^{2} - 3 x + 2}{- x ^{2} - 4 x - 4}

- \frac{7 x - 10}{( x + 2 ) ^{3}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{( 2 x - 3 ) ( - x ^{2} - 4 x - 4 ) - ( - 2 x - 4 ) ( x ^{2} - 3 x + 2 )}{( - x ^{2} - 4 x - 4 ) ^{2}} : - \frac{7 x - 10}{( x + 2 ) ^{3}}

= - \frac{7 x - 10}{( x + 2 ) ^{3}}

\frac{\partial}{\partial x} (ln (sin (x)))

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

\int (x^{2} + x) e^{- 2 x} d x

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

a re a 4 x, x^{2} - 5