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

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

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

The first derivative of (1+1/x ^3) is -(3(x+1)^2)/(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} ((1 + \frac{1}{x})^{3})

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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