derivative of (-6x/((x^2-4)^2))

Lösung

\frac{d}{d x} (\frac{- 6 x}{( x ^{2} - 4 ) ^{2}})

- \frac{6 ( - 3 x ^{2} - 4 )}{( x ^{2} - 4 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{- 6 x}{( x ^{2} - 4 ) ^{2}})

Vereinfache

\frac{- 6 x}{( x ^{2} - 4 ) ^{2}} : - \frac{6 x}{( x ^{2} - 4 ) ^{2}}

= \frac{d}{d x} (- \frac{6 x}{( x ^{2} - 4 ) ^{2}})

Entferne die Konstante:

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

= - 6 \frac{d}{d x} (\frac{x}{( x ^{2} - 4 ) ^{2}})

Wende die Quotientenregel an:

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

= - 6 \cdot \frac{\frac{d x}{d x} ( x ^{2} - 4 ) ^{2} - \frac{d}{d x} ( ( x ^{2} - 4 ) ^{2} ) x}{( ( x ^{2} - 4 ) ^{2} ) ^{2}}

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

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

= - 6 \cdot \frac{1 \cdot ( x ^{2} - 4 ) ^{2} - 4 x ( x ^{2} - 4 ) x}{( ( x ^{2} - 4 ) ^{2} ) ^{2}}

Vereinfache

- 6 \cdot \frac{1 \cdot ( x ^{2} - 4 ) ^{2} - 4 x ( x ^{2} - 4 ) x}{( ( x ^{2} - 4 ) ^{2} ) ^{2}} : - \frac{6 ( - 3 x ^{2} - 4 )}{( x ^{2} - 4 ) ^{3}}

= - \frac{6 ( - 3 x ^{2} - 4 )}{( x ^{2} - 4 ) ^{3}}

\int e^{x^{0.5}} d x

\frac{\partial}{\partial x} (a x^{b} y^{(1 - b)})

\frac{d y}{d x} = (- 10 x^{4} y)

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

\frac{d y}{d x} = 4 x^{3} y - y