What is the derivative of sqrt(2x^4-2x) ?

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

What is the first derivative of sqrt(2x^4-2x) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\frac{4 x ^{3} - 1}{2 x ^{4} - 2 x}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 x^{4} - 2 x) = 8 x^{3} - 2

= \frac{1}{2 2 x ^{4} - 2 x} (8 x^{3} - 2)

Simplify

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

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

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