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Popular >

derivative of 5/3 x^{2/3}

Solution

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

Solution

\frac{10}{9 x ^{\frac{1}{3}}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

\frac{5}{3} \cdot \frac{2}{3} x^{\frac{2}{3} - 1} : \frac{10}{9 x ^{\frac{1}{3}}}

= \frac{10}{9 x ^{\frac{1}{3}}}

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Frequently Asked Questions (FAQ)

What is the derivative of 5/3 x^{2/3} ?
The derivative of 5/3 x^{2/3} is (10)/(9x^{1/3)}
What is the first derivative of 5/3 x^{2/3} ?
The first derivative of 5/3 x^{2/3} is (10)/(9x^{1/3)}