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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 0 lim (\frac{5 x ^{2}}{2})

y^{^{'}} + \frac{1}{t} y = \frac{1}{t ^{2}}

f (x) = x^{2} cos (x)

\int e^{(- \frac{x}{4})} d x

x^{2} + x - 8

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