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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int_{0}^{π} sin^{2} (n x) d x

\int 3 (3 x + 9)^{7} d x

n or ma l f (x) = lo g_{2} (2 x^{2} + 14), at x = 5

\frac{d x}{d t} = 2 + 2 x + t + t x

\frac{\partial}{\partial x} (x^{3} + y^{2})