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

The derivative of (2x/(sqrt(x^2+9))) is (18)/((x^2+9)sqrt(x^2+9))

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

The first derivative of (2x/(sqrt(x^2+9))) is (18)/((x^2+9)sqrt(x^2+9))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\frac{18}{( x ^{2} + 9 ) x ^{2} + 9}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

2 \cdot \frac{1 \cdot x ^{2} + 9 - \frac{x}{x ^{2} + 9} x}{( x ^{2} + 9 ) ^{2}} : \frac{18}{( x ^{2} + 9 ) x ^{2} + 9}

= \frac{18}{( x ^{2} + 9 ) x ^{2} + 9}

in v erse l a pl a ce \frac{3 s - 15}{2 s ^{2} - 4 s + 10}

t an g e n t f (x) = \frac{2}{x + 7}, (- 8, - 2)

n = 1 \sum \infty (sin (8))^{n}

x \to 0 + lim (4 + ln (x))

e^{x} y \frac{d y}{d x} = e^{- y} + e^{- 5 x - y}

What is the derivative of (2x/(sqrt(x^2+9))) ?
The derivative of (2x/(sqrt(x^2+9))) is (18)/((x^2+9)sqrt(x^2+9))
What is the first derivative of (2x/(sqrt(x^2+9))) ?
The first derivative of (2x/(sqrt(x^2+9))) is (18)/((x^2+9)sqrt(x^2+9))