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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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