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

The derivative of 2/((1+x^3)) is -6/((1+x)^4)

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

The first derivative of 2/((1+x^3)) is -6/((1+x)^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

- \frac{6}{( 1 + x ) ^{4}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

2 (- \frac{3}{( 1 + x ) ^{4}} \cdot 1) : - \frac{6}{( 1 + x ) ^{4}}

= - \frac{6}{( 1 + x ) ^{4}}

What is the derivative of 2/((1+x^3)) ?
The derivative of 2/((1+x^3)) is -6/((1+x)^4)
What is the first derivative of 2/((1+x^3)) ?
The first derivative of 2/((1+x^3)) is -6/((1+x)^4)