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

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

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

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

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Popular >

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

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

Solution steps

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

Apply the chain rule:

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

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

e^{- 3 x^{2}}

\int \frac{1}{4 t} d t

x \to 6 lim (f (x) - g (x))

\frac{d ^{2}}{d x ^{2}} (6 cos (3 x + 3))

\frac{1}{s ^{2} - 4}

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