derivative of (9x^2+4/(x^2+1))

Lösung

\frac{d}{d x} (\frac{9 x ^{2} + 4}{x ^{2} + 1})

\frac{10 x}{( x ^{2} + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{9 x ^{2} + 4}{x ^{2} + 1})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 9 x ^{2} + 4 ) ( x ^{2} + 1 ) - \frac{d}{d x} ( x ^{2} + 1 ) ( 9 x ^{2} + 4 )}{( x ^{2} + 1 ) ^{2}}

\frac{d}{d x} (9 x^{2} + 4) = 18 x

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

= \frac{18 x ( x ^{2} + 1 ) - 2 x ( 9 x ^{2} + 4 )}{( x ^{2} + 1 ) ^{2}}

Multipliziere aus

18 x (x^{2} + 1) - 2 x (9 x^{2} + 4) : 10 x

= \frac{10 x}{( x ^{2} + 1 ) ^{2}}

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

\int x (3 x - 2) d x

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

\int \frac{2 x ^{3} + 2 x ^{2} + 2 x + 1}{x ^{2} + x} d x

t an g e n t y = 4 x^{3} - 2 x