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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

3 y y^{^{'}} + 2 x = 0

\frac{d}{d x} \frac{5}{( 7 - x ^{2} ) ^{5}}

12 x^{5} - 8 x^{4} + 20 x^{3}

\frac{d}{d x} (\frac{sin ( 2 x + 1 )}{cos ( - 1 - 2 x )})

\frac{d ^{2}}{d x ^{2}} (cos (6 x))

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