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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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