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+9))

Solution

derivative of

\frac{x}{x + 9}

Solution

\frac{9}{2 x ( x + 9 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{x}{x + 9})

Apply the chain rule:

\frac{1}{2 \frac{x}{x + 9}} \frac{d}{d x} (\frac{x}{x + 9})

= \frac{1}{2 \frac{x}{x + 9}} \frac{d}{d x} (\frac{x}{x + 9})

\frac{d}{d x} (\frac{x}{x + 9}) = \frac{9}{( x + 9 ) ^{2}}

= \frac{1}{2 \frac{x}{x + 9}} \cdot \frac{9}{( x + 9 ) ^{2}}

Simplify

\frac{1}{2 \frac{x}{x + 9}} \cdot \frac{9}{( x + 9 ) ^{2}} : \frac{9}{2 x ( x + 9 ) ^{\frac{3}{2}}}

= \frac{9}{2 x ( x + 9 ) ^{\frac{3}{2}}}

Popular Examples

derivative of 1/((1-x^2))

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

integral from 0 to 1 of x/((x+1)(x^2+1))

\int_{0}^{1} \frac{x}{( x + 1 ) ( x ^{2} + 1 )} d x

integral from 0 to 1 of arctan(2x)

\int_{0}^{1} arctan (2 x) d x

integral of x(x-5)^2

\int x (x - 5)^{2} d x

derivative of 3/(6x^{-2})

\frac{d}{d x} (\frac{3}{6 x ^{- 2}})

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x/(x+9)) ?
The derivative of sqrt(x/(x+9)) is 9/(2sqrt(x)(x+9)^{3/2)}
What is the first derivative of sqrt(x/(x+9)) ?
The first derivative of sqrt(x/(x+9)) is 9/(2sqrt(x)(x+9)^{3/2)}