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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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