What is the derivative of x^{4/3}-x^{1/3} ?

The derivative of x^{4/3}-x^{1/3} is (4x-1)/(3x^{2/3)}

What is the first derivative of x^{4/3}-x^{1/3} ?

The first derivative of x^{4/3}-x^{1/3} is (4x-1)/(3x^{2/3)}

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\frac{d}{d x} (x^{\frac{4}{3}} - x^{\frac{1}{3}})

\frac{4 x - 1}{3 x ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (x^{\frac{4}{3}} - x^{\frac{1}{3}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{\frac{4}{3}}) - \frac{d}{d x} (x^{\frac{1}{3}})

\frac{d}{d x} (x^{\frac{4}{3}}) = \frac{4 x ^{\frac{1}{3}}}{3}

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

= \frac{4 x ^{\frac{1}{3}}}{3} - \frac{1}{3 x ^{\frac{2}{3}}}

Simplify

\frac{4 x ^{\frac{1}{3}}}{3} - \frac{1}{3 x ^{\frac{2}{3}}} : \frac{4 x - 1}{3 x ^{\frac{2}{3}}}

= \frac{4 x - 1}{3 x ^{\frac{2}{3}}}

What is the derivative of x^{4/3}-x^{1/3} ?
The derivative of x^{4/3}-x^{1/3} is (4x-1)/(3x^{2/3)}
What is the first derivative of x^{4/3}-x^{1/3} ?
The first derivative of x^{4/3}-x^{1/3} is (4x-1)/(3x^{2/3)}