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

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

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

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

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derivative of

y = x^{\frac{5}{3}} - x^{\frac{2}{3}}

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

x \to - 4 lim (x (x + 3) (x + 2))

\frac{x}{- 6 x + 6}

3 sin (x), 3 cos (x)

y^{^{'}} = t^{2} y^{3}

y^{^{'''}} - 3 y^{^{''}} - 9 y^{^{'}} + 27 y = 0

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