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

The derivative of (sqrt(x))/(3+x) is (3-x)/(2sqrt(x)(3+x)^2)

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

The first derivative of (sqrt(x))/(3+x) is (3-x)/(2sqrt(x)(3+x)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{x}{3 + x}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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