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}}

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\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}}}

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}}