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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

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

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

\frac{\partial}{\partial x} (z - x)

\frac{d x}{d t} = x - 8

f (x) = (8 (x^{3} - 6 x^{2} + 12 x))

\frac{\partial}{\partial x} (\frac{cos ( x ^{2} \cdot y )}{z ^{3}})

\frac{d y}{d x}, 5 x y^{5} + 3 x y = 24

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