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

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

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

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

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derivative of

f (x) = 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}}}

e^{- t} t

\frac{1}{x - 3}

\int \frac{2 e ^{2 r}}{7 + e ^{2 r}} d r

\frac{d}{d x} (5^{6^{7^{x}}})

e^{x} y \cdot y^{^{'}} = e^{- y} + e^{- 2 x - y}

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