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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

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

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

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

Vereinfache

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

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

d er i v a t i v e \frac{6}{r ^{3}}

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

\int \frac{ln ( n )}{n ^{2}}

d er i v a t i v e \frac{4}{5 x + 1}

y^{^{''}} - y^{^{'}} + y = 7 sin (t)