derivative f(x)= x/(x^2+3)

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d x}{d x} = 1

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

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

1 \cdot (x^{2} + 3) - 2 xx = - x^{2} + 3

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

ma c l a u r in \frac{( z - 2 )}{z - 1}

d er i v a t i v e y = 5 - 2 t

\int_{0}^{1} (x - 1)^{3} - (x - 1) d x

in v erse l a pl a ce \frac{1}{s \cdot ( s ^{2} + \frac{9}{2} s + 15 )}

\int 2 - 1 (e - x + 2) d x