What is the derivative of \sqrt[3]{4x} ?

The derivative of \sqrt[3]{4x} is (4^{1/3})/(3x^{2/3)}

What is the first derivative of \sqrt[3]{4x} ?

The first derivative of \sqrt[3]{4x} is (4^{1/3})/(3x^{2/3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

Solution steps

Apply the chain rule:

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

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

\frac{d}{d x} (4 x) = 4

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

Simplify

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

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

What is the derivative of \sqrt[3]{4x} ?
The derivative of \sqrt[3]{4x} is (4^{1/3})/(3x^{2/3)}
What is the first derivative of \sqrt[3]{4x} ?
The first derivative of \sqrt[3]{4x} is (4^{1/3})/(3x^{2/3)}