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

Lösung

ableitung von

\frac{4 x}{x ^{2} + 1}

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (\frac{( x + a ) ^{3}}{b} - c)

\int \frac{- x}{x + 1 - x + 1} d x

\int \frac{6 x - 1}{x ^{3} ( 2 x - 1 )} d x

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

\frac{\partial}{\partial x} (- x - x^{3} sin (2 y))