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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

x \to 1 lim (\frac{x ^{3} + 1}{x + 1})

y^{^{'}} = \frac{x ^{2} + 3 x + 2}{y - 2}

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

\frac{\partial}{\partial y} (e^{y} \cdot sin (x))

f (x) = \frac{1}{2 x + !}

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