What is the derivative of 8(x-1/x)^3 ?

The derivative of 8(x-1/x)^3 is 24x^2+(24)/(x^4)-(24)/(x^2)-24

What is the first derivative of 8(x-1/x)^3 ?

The first derivative of 8(x-1/x)^3 is 24x^2+(24)/(x^4)-(24)/(x^2)-24

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

8 (x - \frac{1}{x})^{3}

24 x^{2} + \frac{24}{x ^{4}} - \frac{24}{x ^{2}} - 24

Solution steps

\frac{d}{d x} (8 (x - \frac{1}{x})^{3})

Take the constant out:

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

= 8 \frac{d}{d x} ((x - \frac{1}{x})^{3})

Apply the chain rule:

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

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

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

= 8 \cdot 3 (x - \frac{1}{x})^{2} (1 + \frac{1}{x ^{2}})

Simplify

8 \cdot 3 (x - \frac{1}{x})^{2} (1 + \frac{1}{x ^{2}}) : 24 x^{2} + \frac{24}{x ^{4}} - \frac{24}{x ^{2}} - 24

= 24 x^{2} + \frac{24}{x ^{4}} - \frac{24}{x ^{2}} - 24

\int 6 x^{2} - 8 x + 3 d x

x^{3} (3 - x)^{4}

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

\frac{d}{d x} (100 + x^{2})

y = x 6^{x}

What is the derivative of 8(x-1/x)^3 ?
The derivative of 8(x-1/x)^3 is 24x^2+(24)/(x^4)-(24)/(x^2)-24
What is the first derivative of 8(x-1/x)^3 ?
The first derivative of 8(x-1/x)^3 is 24x^2+(24)/(x^4)-(24)/(x^2)-24