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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (3 x^{2} + 1) = 6 x

= \frac{1 \cdot ( 3 x ^{2} + 1 ) - 6 xx}{( 3 x ^{2} + 1 ) ^{2}}

1 \cdot (3 x^{2} + 1) - 6 xx = - 3 x^{2} + 1

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

(cos^{4} (x))^{^{'}}

x \to 0 lim (\frac{sin ( - 4 x )}{x})

\int \frac{x ^{6}}{x ^{14} - 9} d x

d er i v a t i v e 4 + 3 x

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