What is the derivative of (x^2-1^{1/3}) ?

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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