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

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

\frac{- 2 x}{x ^{2} + 1} : - \frac{2 x}{x ^{2} + 1}

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

Entferne die Konstante:

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

= - 2 \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}}

= - 2 \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

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

Vereinfache

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

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

\int 12 e^{3 x - 1} d x

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

x \to 2 lim (2 x^{2} - 4 x)

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

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