derivative of (3x^2+4x+3/(x^2+1))

Lösung

\frac{d}{d x} (\frac{3 x ^{2} + 4 x + 3}{x ^{2} + 1})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x ^{2} + 4 x + 3}{x ^{2} + 1})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 x ^{2} + 4 x + 3 ) ( x ^{2} + 1 ) - \frac{d}{d x} ( x ^{2} + 1 ) ( 3 x ^{2} + 4 x + 3 )}{( x ^{2} + 1 ) ^{2}}

\frac{d}{d x} (3 x^{2} + 4 x + 3) = 6 x + 4

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

= \frac{( 6 x + 4 ) ( x ^{2} + 1 ) - 2 x ( 3 x ^{2} + 4 x + 3 )}{( x ^{2} + 1 ) ^{2}}

Multipliziere aus

(6 x + 4) (x^{2} + 1) - 2 x (3 x^{2} + 4 x + 3) : - 4 x^{2} + 4

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

d er i v a t i v e 2 sec (x) + 5 cot (x)

\int_{0}^{π} 2 cos^{2} (\frac{x}{2}) d x

\frac{\partial}{\partial y} (x yz)

y^{^{''}} + 5 y^{^{'}} + 11 y = 33

\frac{d y}{d t} = 3 cos (t) - 5 y