What is the derivative of x^{1/3}-x^{-2/3} ?

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

x \to + 0 lim (2 x^{2} cos (\frac{5}{x}))

\frac{\partial}{\partial x} (e^{x} - 2 - cos (x y))

\frac{d}{d x} (\frac{3}{5 + x})

\int \frac{1}{x + 4} d x

y^{^{'}} = \frac{2 cos ( y )}{sin ( y )}

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