derivative (3x^4+6)/(x^2)

Lösung

ableitung von

\frac{3 x ^{4} + 6}{x ^{2}}

\frac{6 ( x ^{4} - 2 )}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x ^{4} + 6}{x ^{2}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 x ^{4} + 6 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 3 x ^{4} + 6 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (3 x^{4} + 6) = 12 x^{3}

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

= \frac{12 x ^{3} x ^{2} - 2 x ( 3 x ^{4} + 6 )}{( x ^{2} ) ^{2}}

Vereinfache

\frac{12 x ^{3} x ^{2} - 2 x ( 3 x ^{4} + 6 )}{( x ^{2} ) ^{2}} : \frac{6 ( x ^{4} - 2 )}{x ^{3}}

= \frac{6 ( x ^{4} - 2 )}{x ^{3}}

\frac{\partial}{\partial x} (- t + x)

t y^{^{'}} = 2 y - 3 t^{3} cos (4 t)

\frac{\partial}{\partial x} (6 x y - 6 x)

x^{2} y^{^{''}} - 3 x y^{^{'}} - 2 y = 0

x \to - \frac{π}{3} lim (- sec (x))