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 >

\frac{d}{d x} (\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}}

\int 18 - x^{2} d x

\frac{d}{d x} (arccot (3 x))

x^{\frac{5}{3}} - x^{\frac{2}{3}}

x - 3

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

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)