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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{2}^{4} 5 t^{2} d t

\frac{d}{d x} ((2 x - 3)^{2} (5 x^{2} + 2)^{3})

\frac{d}{d x} (- 8 cos (- 4 x - 3))

\frac{1}{s ( s + 2 ) ^{2}}

\int \frac{x ^{2} + 4}{3 x ^{3} - 4 x ^{2} - 4 x} d x

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