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^x/(4x^2+9))

Lösung

\frac{d}{d x} (\frac{e ^{x}}{4 x ^{2} + 9})

Lösung

\frac{e ^{x} ( 4 x ^{2} + 9 ) - 8 x e ^{x}}{( 4 x ^{2} + 9 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{e ^{x}}{4 x ^{2} + 9})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( e ^{x} ) ( 4 x ^{2} + 9 ) - \frac{d}{d x} ( 4 x ^{2} + 9 ) e ^{x}}{( 4 x ^{2} + 9 ) ^{2}}

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

\frac{d}{d x} (4 x^{2} + 9) = 8 x

= \frac{e ^{x} ( 4 x ^{2} + 9 ) - 8 x e ^{x}}{( 4 x ^{2} + 9 ) ^{2}}

Graph

Beliebte Beispiele

integral of 3e^6

\int 3 e^{6} d x

(\partial)/(\partial x)(x^3yz^2+3yz)

\frac{\partial}{\partial x} (x^{3} y z^{2} + 3 yz)

tangent f(x)=(x^3-7)(3x^2+5)

t an g e n t f (x) = (x^{3} - 7) (3 x^{2} + 5)

x^{^{'}} = a x + b

integral of xe^{(-x)/4}

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