What is (\partial)/(\partial x)(-(2x)/((1+x^2)^2)) ?

The answer to (\partial)/(\partial x)(-(2x)/((1+x^2)^2)) is -(2(-3x^2+1))/((1+x^2)^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(-(2x)/((1+x^2)^2))

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

\frac{\partial}{\partial x} (x) = 1

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

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

Simplify

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

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

x y^{^{'}} + 2 y = \frac{sin ( x )}{x}

y^{^{'}} = 7 x e^{y}

(1 + x^{2}) y + x y^{^{'}} + a x = 0

k \to 0 lim (\frac{x ^{2} k + 3 x k ^{2} + k ^{3}}{2 x k + 5 k ^{2}})

\frac{d}{d x} (\frac{1 + x}{1 + e ^{x}})

What is (\partial)/(\partial x)(-(2x)/((1+x^2)^2)) ?
The answer to (\partial)/(\partial x)(-(2x)/((1+x^2)^2)) is -(2(-3x^2+1))/((1+x^2)^3)