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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\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}}}

\frac{\partial}{\partial v} (\frac{1}{3} (v - 2 u))

\int (7 - x)^{49} d x

\int (x^{2} + 2)^{2} d x

\int \frac{tan ^{2} ( x ) + sec ^{2} ( x )}{tan ( x )} d x

\int \frac{2 x}{x ^{4} + 1} d x

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)}