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

Lösung

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

\frac{8 x}{( x ^{2} + 1 ) ^{2}}

Schritte zur Lösung

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

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

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

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

Multipliziere aus

2 x (x^{2} + 1) - 2 x (x^{2} - 3) : 8 x

= \frac{8 x}{( x ^{2} + 1 ) ^{2}}

\int_{1}^{5} t^{3} ln (4 t) d t

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

d er i v a t i v e 3 x^{- \frac{1}{2}}

\frac{d}{d x} ((7 arcsin (4 x))^{x})

\frac{\partial}{\partial x} (\frac{z x - y}{x})