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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (1) = 0

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

= 0 - (- \frac{2}{3 x ^{\frac{5}{3}}})

Simplify

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

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