What is the derivative of (6^{2/3}-x^{2/3}^{3/2}) ?

The derivative of (6^{2/3}-x^{2/3}^{3/2}) is -((6^{2/3}-x^{2/3})^{1/2})/(x^{1/3)}

What is the first derivative of (6^{2/3}-x^{2/3}^{3/2}) ?

The first derivative of (6^{2/3}-x^{2/3}^{3/2}) is -((6^{2/3}-x^{2/3})^{1/2})/(x^{1/3)}

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

- \frac{( 6 ^{\frac{2}{3}} - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{x ^{\frac{1}{3}}}

Solution steps

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

Apply the chain rule:

\frac{3 ( 6 ^{\frac{2}{3}} - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (6^{\frac{2}{3}} - x^{\frac{2}{3}})

= \frac{3 ( 6 ^{\frac{2}{3}} - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (6^{\frac{2}{3}} - x^{\frac{2}{3}})

\frac{d}{d x} (6^{\frac{2}{3}} - x^{\frac{2}{3}}) = - \frac{2}{3 x ^{\frac{1}{3}}}

= \frac{3 ( 6 ^{\frac{2}{3}} - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{2} (- \frac{2}{3 x ^{\frac{1}{3}}})

Simplify

\frac{3 ( 6 ^{\frac{2}{3}} - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{2} (- \frac{2}{3 x ^{\frac{1}{3}}}) : - \frac{( 6 ^{\frac{2}{3}} - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{x ^{\frac{1}{3}}}

= - \frac{( 6 ^{\frac{2}{3}} - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{x ^{\frac{1}{3}}}

\int \frac{1}{x ^{2} + x + 5} d x

\int e^{3 x - 2} d x

\frac{d y}{d x} - 9 y^{2} e^{- 1 x} = 0, y (0) = 5

y = x^{4}, at x = 0

cos (5 t)

What is the derivative of (6^{2/3}-x^{2/3}^{3/2}) ?
The derivative of (6^{2/3}-x^{2/3}^{3/2}) is -((6^{2/3}-x^{2/3})^{1/2})/(x^{1/3)}
What is the first derivative of (6^{2/3}-x^{2/3}^{3/2}) ?
The first derivative of (6^{2/3}-x^{2/3}^{3/2}) is -((6^{2/3}-x^{2/3})^{1/2})/(x^{1/3)}