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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Take the constant out:

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

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

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

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

\frac{d}{d x} ((x^{2} + 1)^{2}) = 4 x (x^{2} + 1)

= - 2 \cdot \frac{1 \cdot ( x ^{2} + 1 ) ^{2} - 4 x ( x ^{2} + 1 ) x}{( ( x ^{2} + 1 ) ^{2} ) ^{2}}

Simplify

- 2 \cdot \frac{1 \cdot ( x ^{2} + 1 ) ^{2} - 4 x ( x ^{2} + 1 ) x}{( ( x ^{2} + 1 ) ^{2} ) ^{2}} : - \frac{2 ( - 3 x ^{2} + 1 )}{( x ^{2} + 1 ) ^{3}}

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

f (x) = 4 x^{2} - 3 x, at x = - 1

x \to 2 lim (x^{2} + 2 x - 7)

\frac{\partial}{\partial y} (sin (2 y))

\int_{0}^{3} \frac{2 t}{( t - 4 ) ^{2}} d t

\frac{x ^{2} - 3 x + 2}{- x ^{2} - 4 x + 4}

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