de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of (e^{2x}/(x^2))

Lösung

\frac{d}{d x} (\frac{e ^{2 x}}{x ^{2}})

Lösung

\frac{2 e ^{2 x} ( x - 1 )}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{e ^{2 x}}{x ^{2}})

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{e ^{2 x} \cdot 2 x ^{2} - 2 x e ^{2 x}}{( x ^{2} ) ^{2}} : \frac{2 e ^{2 x} ( x - 1 )}{x ^{3}}

= \frac{2 e ^{2 x} ( x - 1 )}{x ^{3}}

Graph

Beliebte Beispiele

integral of x^2-7x+6

\int x^{2} - 7 x + 6 d x

derivative of 2*sin(x*cos(x))

\frac{d}{d x} (2 \cdot sin (x) \cdot cos (x))

integral of sqrt(1+x^{1/2)}

\int 1 + x^{\frac{1}{2}} d x

steigung y=sqrt(7x+11),(2,5)

s l o p e y = 7 x + 11, (2, 5)

laplacetransform e^{3a-bt}

l a pl a ce t r an s f or m e^{3 a - b t}