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Beliebt Rechnen >

derivative of (e^{6x}/x)

Lösung

\frac{d}{d x} (\frac{e ^{6 x}}{x})

Lösung

\frac{6 e ^{6 x} x - e ^{6 x}}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{e ^{6 x}}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( e ^{6 x} ) x - \frac{d x}{d x} e ^{6 x}}{x ^{2}}

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

\frac{d x}{d x} = 1

= \frac{e ^{6 x} \cdot 6 x - 1 \cdot e ^{6 x}}{x ^{2}}

Vereinfache

= \frac{6 e ^{6 x} x - e ^{6 x}}{x ^{2}}

Graph

Beliebte Beispiele

limit as x approaches 3 of x+3

x \to 3 lim (x + 3)

derivative-(18)/(x^3)

d er i v a t i v e - \frac{18}{x ^{3}}

(dy)/(dx)=(xy+y^2+x^2)/(x^2)

\frac{d y}{d x} = \frac{x y + y ^{2} + x ^{2}}{x ^{2}}

integral from-1 to 3 of |x-2x^2|

\int_{- 1}^{3} x - 2 x^{2} d x

(dy}{dx}=\frac{x^3-2y)/x

\frac{d y}{d x} = \frac{x ^{3} - 2 y}{x}