derivative of (-8x/(x^2+1))

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

\frac{- 8 x}{x ^{2} + 1} : - \frac{8 x}{x ^{2} + 1}

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

Entferne die Konstante:

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

= - 8 \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}}

= - 8 \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

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

Vereinfache

- 8 \cdot \frac{1 \cdot ( x ^{2} + 1 ) - 2 xx}{( x ^{2} + 1 ) ^{2}} : - \frac{8 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}

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

a re a y = 3 x^{2} ln (x), y = 12 ln (x)

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

\int 4 - x^{2} d x

\int x e^{11 x} d x

a re a 3 cos (π x), 12 x^{2} - 3, - 0.5, 0.5