What is the derivative of (sqrt(x))/(3(x^2+1)) ?

The derivative of (sqrt(x))/(3(x^2+1)) is (-3x^2+1)/(6sqrt(x)(x^2+1)^2)

What is the first derivative of (sqrt(x))/(3(x^2+1)) ?

The first derivative of (sqrt(x))/(3(x^2+1)) is (-3x^2+1)/(6sqrt(x)(x^2+1)^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}{3 ( x ^{2} + 1 )}

\frac{- 3 x ^{2} + 1}{6 x ( x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{3 ( x ^{2} + 1 )})

Take the constant out:

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

= \frac{1}{3} \frac{d}{d x} (\frac{x}{x ^{2} + 1})

Apply the Quotient Rule:

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

= \frac{1}{3} \cdot \frac{\frac{d}{d x} ( x ) ( x ^{2} + 1 ) - \frac{d}{d x} ( x ^{2} + 1 ) x}{( x ^{2} + 1 ) ^{2}}

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

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

= \frac{1}{3} \cdot \frac{\frac{1}{2 x} ( x ^{2} + 1 ) - 2 x x}{( x ^{2} + 1 ) ^{2}}

Simplify

\frac{1}{3} \cdot \frac{\frac{1}{2 x} ( x ^{2} + 1 ) - 2 x x}{( x ^{2} + 1 ) ^{2}} : \frac{- 3 x ^{2} + 1}{6 x ( x ^{2} + 1 ) ^{2}}

= \frac{- 3 x ^{2} + 1}{6 x ( x ^{2} + 1 ) ^{2}}

(3, 2), (6, 8)

3 x + 2 cos (x)

\int (sin (\frac{x}{2})) d x

sin (x), 3 x, \frac{π}{2}, π

x \to 1 - lim (\frac{x}{x ^{2} - 1})

What is the derivative of (sqrt(x))/(3(x^2+1)) ?
The derivative of (sqrt(x))/(3(x^2+1)) is (-3x^2+1)/(6sqrt(x)(x^2+1)^2)
What is the first derivative of (sqrt(x))/(3(x^2+1)) ?
The first derivative of (sqrt(x))/(3(x^2+1)) is (-3x^2+1)/(6sqrt(x)(x^2+1)^2)