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

The derivative of 2/((x^2+x+1^2)) is -(4(2x+1))/((x^2+x+1)^3)

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

The first derivative of 2/((x^2+x+1^2)) is -(4(2x+1))/((x^2+x+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 ^{2} + x + 1 ) ^{2}})

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial y} (2 y + 1)

(t + 1)^{3} t^{2} + 84

x^{2} arctan (2 x)

e^{x - 1}, 1

f (x) = \frac{4 x ^{2}}{( x ^{2} + x ) ^{3}}

What is the derivative of 2/((x^2+x+1^2)) ?
The derivative of 2/((x^2+x+1^2)) is -(4(2x+1))/((x^2+x+1)^3)
What is the first derivative of 2/((x^2+x+1^2)) ?
The first derivative of 2/((x^2+x+1^2)) is -(4(2x+1))/((x^2+x+1)^3)