derivative of ((x+3(x+1))/(x^2-49))

Lösung

\frac{d}{d x} (\frac{( x + 3 ) ( x + 1 )}{x ^{2} - 49})

\frac{- 4 x ^{2} - 104 x - 196}{( x ^{2} - 49 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{( x + 3 ) ( x + 1 )}{x ^{2} - 49})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( ( x + 3 ) ( x + 1 ) ) ( x ^{2} - 49 ) - \frac{d}{d x} ( x ^{2} - 49 ) ( x + 3 ) ( x + 1 )}{( x ^{2} - 49 ) ^{2}}

\frac{d}{d x} ((x + 3) (x + 1)) = 2 x + 4

\frac{d}{d x} (x^{2} - 49) = 2 x

= \frac{( 2 x + 4 ) ( x ^{2} - 49 ) - 2 x ( x + 3 ) ( x + 1 )}{( x ^{2} - 49 ) ^{2}}

Multipliziere aus

(2 x + 4) (x^{2} - 49) - 2 x (x + 3) (x + 1) : - 4 x^{2} - 104 x - 196

= \frac{- 4 x ^{2} - 104 x - 196}{( x ^{2} - 49 ) ^{2}}

\int_{0}^{1} x cos (π x) d x

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

l a pl a ce t r an s f or m t^{2} e^{- 2 t} sin (3 t + 30)

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

x \to \infty lim (3 x^{3} - 1000 x^{2})