en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (sqrt(x))/(x+3)

Solution

derivative of

\frac{x}{x + 3}

Solution

\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}}

Popular Examples

tangent of (2x-1)^{(2)}ln(2x-1)tangent of

(2 x - 1)^{(2)} ln (2 x - 1)

derivative of arctan(sqrt(x^2-2)+C)

\frac{d}{d x} (arctan (x^{2} - 2) + C)

integral of (sec^2(x))/((1+tan(x))^2)

\int \frac{sec ^{2} ( x )}{( 1 + tan ( x ) ) ^{2}} d x

integral of 1/((x+1)^2(x-2))

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

inverse oflaplace 1/(s^2(s^2+16))inverse laplace

\frac{1}{s ^{2} ( s ^{2} + 16 )}

Frequently Asked Questions (FAQ)

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)