derivative ((x^2-1)^3)/(x^2+2)

Lösung

ableitung von

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

\frac{6 x ( x ^{2} - 1 ) ^{2} ( x ^{2} + 2 ) - 2 x ( x ^{2} - 1 ) ^{3}}{( x ^{2} + 2 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} ((x^{2} - 1)^{3}) = 6 x (x^{2} - 1)^{2}

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

= \frac{6 x ( x ^{2} - 1 ) ^{2} ( x ^{2} + 2 ) - 2 x ( x ^{2} - 1 ) ^{3}}{( x ^{2} + 2 ) ^{2}}

\int (- sec^{2} (x)) d x

\int e^{4 x + 1} d x

y^{^{''}} + 20 y^{^{'}} + 500 y = 12

x \to 2 lim (\frac{x ^{3} + 7 x + 6}{x ^{3} + x ^{2} - 4 x - 4})

\int \frac{1}{2 ^{2} + 3 x ^{2}} d x