What is the derivative of 4-x^{2/3} ?

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

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

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

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\frac{d}{d x} (4 - x^{\frac{2}{3}})

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

Solution steps

\frac{d}{d x} (4 - x^{\frac{2}{3}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (4) - \frac{d}{d x} (x^{\frac{2}{3}})

\frac{d}{d x} (4) = 0

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

= 0 - \frac{2}{3 x ^{\frac{1}{3}}}

Simplify

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

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