What is the derivative of x/(sqrt(9+x^2)) ?

The derivative of x/(sqrt(9+x^2)) is 9/((9+x^2)sqrt(9+x^2))

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

The first derivative of x/(sqrt(9+x^2)) is 9/((9+x^2)sqrt(9+x^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{x}{9 + x ^{2}}

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

\frac{d y}{d x} = - \frac{1}{x + 2}

x \to 3 lim (x (x - 1))

\int \frac{5 e ^{x}}{e ^{2 x} + 4 e ^{x} + 4} d x

\frac{d}{d x} (cos (\frac{π}{2} + \frac{1}{x}))

\frac{1}{x + 4}

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