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

The derivative of 2/(x^2-3/(x^{1/3)}) is (-4x^{4/3}+x^3)/(x^{13/3)}

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

The first derivative of 2/(x^2-3/(x^{1/3)}) is (-4x^{4/3}+x^3)/(x^{13/3)}

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

\frac{- 4 x ^{\frac{4}{3}} + x ^{3}}{x ^{\frac{13}{3}}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

- \frac{4}{x ^{3}} - (- \frac{1}{x ^{\frac{4}{3}}}) : \frac{- 4 x ^{\frac{4}{3}} + x ^{3}}{x ^{\frac{13}{3}}}

= \frac{- 4 x ^{\frac{4}{3}} + x ^{3}}{x ^{\frac{13}{3}}}

What is the derivative of 2/(x^2-3/(x^{1/3)}) ?
The derivative of 2/(x^2-3/(x^{1/3)}) is (-4x^{4/3}+x^3)/(x^{13/3)}
What is the first derivative of 2/(x^2-3/(x^{1/3)}) ?
The first derivative of 2/(x^2-3/(x^{1/3)}) is (-4x^{4/3}+x^3)/(x^{13/3)}