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Beliebt Rechnen >

derivative of (2x^5/(5+3x^4+6x^3+2x+4))

Lösung

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

Lösung

\frac{2 ( 3 x ^{8} + 12 x ^{7} + 8 x ^{5} + 45 x ^{4} )}{( 3 x ^{4} + 6 x ^{3} + 2 x + 9 ) ^{2}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (5 + 3 x^{4} + 6 x^{3} + 2 x + 4) = 12 x^{3} + 18 x^{2} + 2

= 2 \cdot \frac{5 x ^{4} ( 5 + 3 x ^{4} + 6 x ^{3} + 2 x + 4 ) - ( 12 x ^{3} + 18 x ^{2} + 2 ) x ^{5}}{( 5 + 3 x ^{4} + 6 x ^{3} + 2 x + 4 ) ^{2}}

Vereinfache

2 \cdot \frac{5 x ^{4} ( 5 + 3 x ^{4} + 6 x ^{3} + 2 x + 4 ) - ( 12 x ^{3} + 18 x ^{2} + 2 ) x ^{5}}{( 5 + 3 x ^{4} + 6 x ^{3} + 2 x + 4 ) ^{2}} : \frac{2 ( 3 x ^{8} + 12 x ^{7} + 8 x ^{5} + 45 x ^{4} )}{( 3 x ^{4} + 6 x ^{3} + 2 x + 9 ) ^{2}}

= \frac{2 ( 3 x ^{8} + 12 x ^{7} + 8 x ^{5} + 45 x ^{4} )}{( 3 x ^{4} + 6 x ^{3} + 2 x + 9 ) ^{2}}

Graph

Beliebte Beispiele

limit as z approaches 0 of (2z-8) 1/3

z \to 0 lim ((2 z - 8) \frac{1}{3})

derivative of (2x/(3-tan(x)))

\frac{d}{d x} (\frac{2 x}{3 - tan ( x )})

d er i v a t i v e - 3 x

(\partial)/(\partial y)(xyln(x^2+y^2))

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

integral of 2/(sqrt(4-x^2))

\int \frac{2}{4 - x ^{2}} d x