derivative g(x)=(2x+2)/(x^2+2)

Lösung

ableitung von

g (x) = \frac{2 x + 2}{x ^{2} + 2}

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

Schritte zur Lösung

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

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

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

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

Multipliziere aus

2 (x^{2} + 2) - 2 x (2 x + 2) : - 2 x^{2} - 4 x + 4

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

n = 0 \sum \infty n

(x, y) \to (- 6, 5) lim (\frac{x ^{2} cos ( π y )}{e ^{x + y}})

\frac{d ^{2}}{d x ^{2}} (cos (π x))

\int \frac{8}{x ^{2} + 9} d x

in v erse l a pl a ce \frac{1}{4 s + 7}