derivative of (-x^2-5/((x^2-5)^2))

Lösung

\frac{d}{d x} (\frac{- x ^{2} - 5}{( x ^{2} - 5 ) ^{2}})

- \frac{2 x ( - x ^{2} - 15 )}{( x ^{2} - 5 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{- x ^{2} - 5}{( x ^{2} - 5 ) ^{2}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( - x ^{2} - 5 ) ( x ^{2} - 5 ) ^{2} - \frac{d}{d x} ( ( x ^{2} - 5 ) ^{2} ) ( - x ^{2} - 5 )}{( ( x ^{2} - 5 ) ^{2} ) ^{2}}

\frac{d}{d x} (- x^{2} - 5) = - 2 x

\frac{d}{d x} ((x^{2} - 5)^{2}) = 4 x (x^{2} - 5)

= \frac{( - 2 x ) ( x ^{2} - 5 ) ^{2} - 4 x ( x ^{2} - 5 ) ( - x ^{2} - 5 )}{( ( x ^{2} - 5 ) ^{2} ) ^{2}}

Vereinfache

\frac{( - 2 x ) ( x ^{2} - 5 ) ^{2} - 4 x ( x ^{2} - 5 ) ( - x ^{2} - 5 )}{( ( x ^{2} - 5 ) ^{2} ) ^{2}} : - \frac{2 x ( - x ^{2} - 15 )}{( x ^{2} - 5 ) ^{3}}

= - \frac{2 x ( - x ^{2} - 15 )}{( x ^{2} - 5 ) ^{3}}

\int e^{2 x} - x e^{2 x} d x

\frac{d}{d x} (- 7 csc (x) + \frac{1}{x ^{5}})

d er i v a t i v e arcsin (\frac{x}{a})

d er i v a t i v e (\frac{4}{3}) π x^{3}

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