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Beliebt Rechnen >

derivative of (e^{4x}/(x^{20)})

Lösung

\frac{d}{d x} (\frac{e ^{4 x}}{x ^{20}})

Lösung

\frac{4 e ^{4 x} ( x - 5 )}{x ^{21}}

Schritte zur Lösung

\frac{d}{d x} (\frac{e ^{4 x}}{x ^{20}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( e ^{4 x} ) x ^{20} - \frac{d}{d x} ( x ^{20} ) e ^{4 x}}{( x ^{20} ) ^{2}}

\frac{d}{d x} (e^{4 x}) = e^{4 x} \cdot 4

\frac{d}{d x} (x^{20}) = 20 x^{19}

= \frac{e ^{4 x} \cdot 4 x ^{20} - 20 x ^{19} e ^{4 x}}{( x ^{20} ) ^{2}}

Vereinfache

\frac{e ^{4 x} \cdot 4 x ^{20} - 20 x ^{19} e ^{4 x}}{( x ^{20} ) ^{2}} : \frac{4 e ^{4 x} ( x - 5 )}{x ^{21}}

= \frac{4 e ^{4 x} ( x - 5 )}{x ^{21}}

Graph

Beliebte Beispiele

derivative of 25xsin(11x)

\frac{d}{d x} (25 x sin (11 x))

integral of 3x^2e^{x^3}

\int 3 x^{2} e^{x^{3}} d x

derivative of 3sqrt(x)-6x

\frac{d}{d x} (3 x - 6 x)

integral from 1 to infinity of 1/(x^3)

\int_{1}^{\infty} \frac{1}{x ^{3}} d x

derivative of x^2y^5

\frac{d}{d x} (x^{2} y^{5})