What is the derivative of y=sqrt(x/(x+9)) ?

The derivative of y=sqrt(x/(x+9)) is 9/(2sqrt(x)(x+9)^{3/2)}

What is the first derivative of y=sqrt(x/(x+9)) ?

The first derivative of y=sqrt(x/(x+9)) is 9/(2sqrt(x)(x+9)^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = \frac{x}{x + 9}

\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}}}

\frac{s + 1}{s ^{2} + 3 s + 2}

\frac{\partial}{\partial y} (e^{x} ln (x y))

\int e^{\frac{x}{10}} d x

\int 3 x^{2} + 3 x^{2} ln (y) d x

\int_{1}^{4} (6 x + x) d x

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