derivative (2x^4+5)/(x^2)

Lösung

ableitung von

\frac{2 x ^{4} + 5}{x ^{2}}

\frac{2 ( 2 x ^{4} - 5 )}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x ^{4} + 5}{x ^{2}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 2 x ^{4} + 5 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 2 x ^{4} + 5 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (2 x^{4} + 5) = 8 x^{3}

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

= \frac{8 x ^{3} x ^{2} - 2 x ( 2 x ^{4} + 5 )}{( x ^{2} ) ^{2}}

Vereinfache

\frac{8 x ^{3} x ^{2} - 2 x ( 2 x ^{4} + 5 )}{( x ^{2} ) ^{2}} : \frac{2 ( 2 x ^{4} - 5 )}{x ^{3}}

= \frac{2 ( 2 x ^{4} - 5 )}{x ^{3}}

\int 6 cos (x) - \frac{9}{1 - x ^{2}} d x

\int - 2 e^{- \frac{1}{2} x} d x

l a pl a ce t r an s f or m 3 sin (5 t + 4 5^{\circ})

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

\frac{d}{d x} (\frac{1}{4 - x})