derivative of (2x^5+3x/(x^4))

Lösung

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

\frac{2 x ^{4} - 9}{x ^{4}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (2 x^{5} + 3 x) = 10 x^{4} + 3

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

= \frac{( 10 x ^{4} + 3 ) x ^{4} - 4 x ^{3} ( 2 x ^{5} + 3 x )}{( x ^{4} ) ^{2}}

Vereinfache

\frac{( 10 x ^{4} + 3 ) x ^{4} - 4 x ^{3} ( 2 x ^{5} + 3 x )}{( x ^{4} ) ^{2}} : \frac{2 x ^{4} - 9}{x ^{4}}

= \frac{2 x ^{4} - 9}{x ^{4}}

\int (5 x^{4}) d x

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

\frac{df}{d s} = 12 s + \frac{5 s}{9 - s ^{2}}

x \to 0 lim (x^{n})

d er i v a t i v e y = x^{3} cos (x)