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

The derivative of (4-x^{2/3}^{2/3}) is -4/(9x^{1/3)(4-x^{2/3})^{1/3}}

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

The first derivative of (4-x^{2/3}^{2/3}) is -4/(9x^{1/3)(4-x^{2/3})^{1/3}}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

- \frac{4}{9 x ^{\frac{1}{3}} ( 4 - x ^{\frac{2}{3}} ) ^{\frac{1}{3}}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{2}{3 ( 4 - x ^{\frac{2}{3}} ) ^{\frac{1}{3}}} (- \frac{2}{3 x ^{\frac{1}{3}}}) : - \frac{4}{9 x ^{\frac{1}{3}} ( 4 - x ^{\frac{2}{3}} ) ^{\frac{1}{3}}}

= - \frac{4}{9 x ^{\frac{1}{3}} ( 4 - x ^{\frac{2}{3}} ) ^{\frac{1}{3}}}

\frac{d}{d x} (\frac{1}{10 x ^{\frac{9}{10}}})

\int \frac{x - 11}{x ^{2} + 6 x + 25} d x

f (x) = x (7^{- 3 x})

\int \frac{x ^{2} - 7 x + 12}{x - 3} d x

y = \frac{3 x - 9}{2 x + 8}

What is the derivative of (4-x^{2/3}^{2/3}) ?
The derivative of (4-x^{2/3}^{2/3}) is -4/(9x^{1/3)(4-x^{2/3})^{1/3}}
What is the first derivative of (4-x^{2/3}^{2/3}) ?
The first derivative of (4-x^{2/3}^{2/3}) is -4/(9x^{1/3)(4-x^{2/3})^{1/3}}