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

The derivative of (sqrt(x)+1/(sqrt(x)+3)) is 1/(sqrt(x)(\sqrt{x)+3)^2}

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

The first derivative of (sqrt(x)+1/(sqrt(x)+3)) is 1/(sqrt(x)(\sqrt{x)+3)^2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

What is the derivative of (sqrt(x)+1/(sqrt(x)+3)) ?
The derivative of (sqrt(x)+1/(sqrt(x)+3)) is 1/(sqrt(x)(\sqrt{x)+3)^2}
What is the first derivative of (sqrt(x)+1/(sqrt(x)+3)) ?
The first derivative of (sqrt(x)+1/(sqrt(x)+3)) is 1/(sqrt(x)(\sqrt{x)+3)^2}