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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{1}{1 + x + x ^{2} + x ^{3}}

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{18}{( 1 + 3 x ) ^{3}})

\frac{25 s}{( s ^{2} + 9 ) ( s + 4 )}

1 + sin^{2} (x)

y^{^{'}} - \frac{2}{t} y = t^{2}

\frac{d}{d x} (- \frac{8 x}{( 4 x ^{2} + 1 ) ^{2}})

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