What is the derivative of (e^{2x+1})/(2x+5) ?

The derivative of (e^{2x+1})/(2x+5) is (4e^{2x+1}x+8e^{2x+1})/((2x+5)^2)

What is the first derivative of (e^{2x+1})/(2x+5) ?

The first derivative of (e^{2x+1})/(2x+5) is (4e^{2x+1}x+8e^{2x+1})/((2x+5)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{e ^{2 x + 1}}{2 x + 5}

\frac{4 e ^{2 x + 1} x + 8 e ^{2 x + 1}}{( 2 x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{2 x + 1}}{2 x + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{2 x + 1} ) ( 2 x + 5 ) - \frac{d}{d x} ( 2 x + 5 ) e ^{2 x + 1}}{( 2 x + 5 ) ^{2}}

\frac{d}{d x} (e^{2 x + 1}) = e^{2 x + 1} \cdot 2

\frac{d}{d x} (2 x + 5) = 2

= \frac{e ^{2 x + 1} \cdot 2 ( 2 x + 5 ) - 2 e ^{2 x + 1}}{( 2 x + 5 ) ^{2}}

Expand

e^{2 x + 1} \cdot 2 (2 x + 5) - 2 e^{2 x + 1} : 4 e^{2 x + 1} x + 8 e^{2 x + 1}

= \frac{4 e ^{2 x + 1} x + 8 e ^{2 x + 1}}{( 2 x + 5 ) ^{2}}

What is the derivative of (e^{2x+1})/(2x+5) ?
The derivative of (e^{2x+1})/(2x+5) is (4e^{2x+1}x+8e^{2x+1})/((2x+5)^2)
What is the first derivative of (e^{2x+1})/(2x+5) ?
The first derivative of (e^{2x+1})/(2x+5) is (4e^{2x+1}x+8e^{2x+1})/((2x+5)^2)