What is the derivative of (1+x^4)^{2/3} ?

The derivative of (1+x^4)^{2/3} is (8x^3)/(3(1+x^4)^{1/3)}

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

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

\frac{8 x ^{3}}{3 ( 1 + x ^{4} ) ^{\frac{1}{3}}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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