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

The ((4-x^{2/3})^{3/2})^' is -((4-x^{2/3})^{1/2})/(x^{1/3)}

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

The first ((4-x^{2/3})^{3/2})^' is -((4-x^{2/3})^{1/2})/(x^{1/3)}

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = \frac{1 + 2 x}{3 + x}

f (x) = (x - 1) e^{x^{2} - 4}

\frac{d y}{d x}, x y - 4 x = 5

\int - cos (2 x) d x

\frac{x ^{2}}{2 - x ^{2}}

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