(x/(x^2+1))^'

Lösung

(\frac{x}{x ^{2} + 1})^{^{'}}

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

Schritte zur Lösung

(\frac{x}{x ^{2} + 1})^{'}

Wende die Quotientenregel an:

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

= \frac{x ^{^{'}} ( x ^{2} + 1 ) - ( x ^{2} + 1 ) ^{^{'}} x}{( x ^{2} + 1 ) ^{2}}

x^{'} = 1

(x^{2} + 1)^{'} = 2 x

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

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

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

\int cos (x) sin (x) e^{- 2 c o s (x)} d x

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