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

Lösung

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

\frac{24}{x ^{4}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{3 x ^{2} x ^{3} - 3 x ^{2} ( x - 2 ) ( x ^{2} + 2 x + 4 )}{( x ^{3} ) ^{2}} : \frac{24}{x ^{4}}

= \frac{24}{x ^{4}}

\frac{d}{d x} (ln (arctan (7 x^{5})))

\int_{- \infty}^{0} \frac{1}{6 - 7 x} d x

\frac{d}{d x} (x^{2} sin (x^{2}))

\int \frac{1}{x ^{2} + 6 x + 12} d x

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