derivative of ((x+2*(x+4))/(x^2-4x+20))

Lösung

\frac{d}{d x} (\frac{( x + 2 ) \cdot ( x + 4 )}{x ^{2} - 4 x + 20})

\frac{- 10 x ^{2} + 24 x + 152}{( x ^{2} - 4 x + 20 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{( x + 2 ) ( x + 4 )}{x ^{2} - 4 x + 20})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( ( x + 2 ) ( x + 4 ) ) ( x ^{2} - 4 x + 20 ) - \frac{d}{d x} ( x ^{2} - 4 x + 20 ) ( x + 2 ) ( x + 4 )}{( x ^{2} - 4 x + 20 ) ^{2}}

\frac{d}{d x} ((x + 2) (x + 4)) = 2 x + 6

\frac{d}{d x} (x^{2} - 4 x + 20) = 2 x - 4

= \frac{( 2 x + 6 ) ( x ^{2} - 4 x + 20 ) - ( 2 x - 4 ) ( x + 2 ) ( x + 4 )}{( x ^{2} - 4 x + 20 ) ^{2}}

Multipliziere aus

(2 x + 6) (x^{2} - 4 x + 20) - (2 x - 4) (x + 2) (x + 4) : - 10 x^{2} + 24 x + 152

= \frac{- 10 x ^{2} + 24 x + 152}{( x ^{2} - 4 x + 20 ) ^{2}}

\frac{\partial}{\partial y} (x y e^{(x y)})

d er i v a t i v e f (x) = 3 x^{2} - 4 x + 1

\frac{d}{d x} (sin (x) sec (x))

\int_{- 2}^{2} 2 d x

d er i v a t i v e y = 3 x^{2} sin (x)