What is the derivative of (3x+1/(sqrt(x+1))) ?

The derivative of (3x+1/(sqrt(x+1))) is (3x+5)/(2(x+1)sqrt(x+1))

What is the first derivative of (3x+1/(sqrt(x+1))) ?

The first derivative of (3x+1/(sqrt(x+1))) is (3x+5)/(2(x+1)sqrt(x+1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (\frac{3 x + 1}{x + 1})

\frac{3 x + 5}{2 ( x + 1 ) x + 1}

Solution steps

\frac{d}{d x} (\frac{3 x + 1}{x + 1})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (3 x + 1) = 3

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

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

Simplify

\frac{3 x + 1 - \frac{1}{2 x + 1} ( 3 x + 1 )}{( x + 1 ) ^{2}} : \frac{3 x + 5}{2 ( x + 1 ) x + 1}

= \frac{3 x + 5}{2 ( x + 1 ) x + 1}

What is the derivative of (3x+1/(sqrt(x+1))) ?
The derivative of (3x+1/(sqrt(x+1))) is (3x+5)/(2(x+1)sqrt(x+1))
What is the first derivative of (3x+1/(sqrt(x+1))) ?
The first derivative of (3x+1/(sqrt(x+1))) is (3x+5)/(2(x+1)sqrt(x+1))