What is the derivative of (e^x/(4x^2+9)) ?

The derivative of (e^x/(4x^2+9)) is (e^x(4x^2+9)-8xe^x)/((4x^2+9)^2)

What is the first derivative of (e^x/(4x^2+9)) ?

The first derivative of (e^x/(4x^2+9)) is (e^x(4x^2+9)-8xe^x)/((4x^2+9)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the Quotient Rule:

(\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}}

\int 3 e^{6} d x

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

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

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

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

What is the derivative of (e^x/(4x^2+9)) ?
The derivative of (e^x/(4x^2+9)) is (e^x(4x^2+9)-8xe^x)/((4x^2+9)^2)
What is the first derivative of (e^x/(4x^2+9)) ?
The first derivative of (e^x/(4x^2+9)) is (e^x(4x^2+9)-8xe^x)/((4x^2+9)^2)