What is the derivative of 5x^{1/3}-5x^{-2/3} ?

The derivative of 5x^{1/3}-5x^{-2/3} is 5/(3x^{2/3)}+(10)/(3x^{5/3)}

What is the first derivative of 5x^{1/3}-5x^{-2/3} ?

The first derivative of 5x^{1/3}-5x^{-2/3} is 5/(3x^{2/3)}+(10)/(3x^{5/3)}

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derivative of

5 x^{\frac{1}{3}} - 5 x^{- \frac{2}{3}}

\frac{5}{3 x ^{\frac{2}{3}}} + \frac{10}{3 x ^{\frac{5}{3}}}

Solution steps

\frac{d}{d x} (5 x^{\frac{1}{3}} - 5 x^{- \frac{2}{3}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (5 x^{\frac{1}{3}}) - \frac{d}{d x} (5 x^{- \frac{2}{3}})

\frac{d}{d x} (5 x^{\frac{1}{3}}) = \frac{5}{3 x ^{\frac{2}{3}}}

\frac{d}{d x} (5 x^{- \frac{2}{3}}) = - \frac{10}{3 x ^{\frac{5}{3}}}

= \frac{5}{3 x ^{\frac{2}{3}}} - (- \frac{10}{3 x ^{\frac{5}{3}}})

Simplify

= \frac{5}{3 x ^{\frac{2}{3}}} + \frac{10}{3 x ^{\frac{5}{3}}}

What is the derivative of 5x^{1/3}-5x^{-2/3} ?
The derivative of 5x^{1/3}-5x^{-2/3} is 5/(3x^{2/3)}+(10)/(3x^{5/3)}
What is the first derivative of 5x^{1/3}-5x^{-2/3} ?
The first derivative of 5x^{1/3}-5x^{-2/3} is 5/(3x^{2/3)}+(10)/(3x^{5/3)}