derivative of (x^3-8/(x^2-4))

Lösung

\frac{d}{d x} (\frac{x ^{3} - 8}{x ^{2} - 4})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{3} - 8}{x ^{2} - 4})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{3} - 8 ) ( x ^{2} - 4 ) - \frac{d}{d x} ( x ^{2} - 4 ) ( x ^{3} - 8 )}{( x ^{2} - 4 ) ^{2}}

\frac{d}{d x} (x^{3} - 8) = 3 x^{2}

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

= \frac{3 x ^{2} ( x ^{2} - 4 ) - 2 x ( x ^{3} - 8 )}{( x ^{2} - 4 ) ^{2}}

Vereinfache

\frac{3 x ^{2} ( x ^{2} - 4 ) - 2 x ( x ^{3} - 8 )}{( x ^{2} - 4 ) ^{2}} : \frac{x ( x + 4 )}{( x + 2 ) ^{2}}

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

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

\frac{d}{d x} ((5 + x^{4})^{12})

\int \frac{1}{v ^{2} + 1} d v

in v erse l a pl a ce \frac{2 s + 1}{3 s ^{2} + 5 s}

\frac{d}{d x} (ln (ln (3 x^{9})))