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Beliebt Rechnen >

derivative of (4x^5+6/(x^3))

Lösung

\frac{d}{d x} (\frac{4 x ^{5} + 6}{x ^{3}})

Lösung

\frac{2 ( 4 x ^{5} - 9 )}{x ^{4}}

Schritte zur Lösung

\frac{d}{d x} (\frac{4 x ^{5} + 6}{x ^{3}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 4 x ^{5} + 6 ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ( 4 x ^{5} + 6 )}{( x ^{3} ) ^{2}}

\frac{d}{d x} (4 x^{5} + 6) = 20 x^{4}

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

= \frac{20 x ^{4} x ^{3} - 3 x ^{2} ( 4 x ^{5} + 6 )}{( x ^{3} ) ^{2}}

Vereinfache

\frac{20 x ^{4} x ^{3} - 3 x ^{2} ( 4 x ^{5} + 6 )}{( x ^{3} ) ^{2}} : \frac{2 ( 4 x ^{5} - 9 )}{x ^{4}}

= \frac{2 ( 4 x ^{5} - 9 )}{x ^{4}}

Graph

Beliebte Beispiele

d er i v a t i v e - \frac{5}{x}

fläche x,x^2,[0,1]

a re a x, x^{2}, [0, 1]

limit as x approaches infinity of x*3

x \to \infty lim (x \cdot 3)

tangent sqrt(x)+sqrt(y)=5

t an g e n t x + y = 5

integral of 2sin(x)-cos(x)

\int 2 sin (x) - cos (x) d x