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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int x \cdot 1 - x^{2} d x

d er i v a t i v e f (x) = 2 x^{2} - 3 x + 6

d er i v a t i v e f (x) = lo g_{2} (x^{2} + 1) - 2^{3}

\frac{\partial}{\partial x} (y + 3)

\int p (p + 6)^{8} d p