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

The derivative of 1/(2sqrt(x)+1/(3x^{2/3)}) is -1/(4x^{3/2)}-2/(9x^{5/3)}

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

The first derivative of 1/(2sqrt(x)+1/(3x^{2/3)}) is -1/(4x^{3/2)}-2/(9x^{5/3)}

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

- \frac{1}{4 x ^{\frac{3}{2}}} - \frac{2}{9 x ^{\frac{5}{3}}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (\frac{1}{2 x}) = - \frac{1}{4 x ^{\frac{3}{2}}}

\frac{d}{d x} (\frac{1}{3 x ^{\frac{2}{3}}}) = - \frac{2}{9 x ^{\frac{5}{3}}}

= - \frac{1}{4 x ^{\frac{3}{2}}} - \frac{2}{9 x ^{\frac{5}{3}}}

What is the derivative of 1/(2sqrt(x)+1/(3x^{2/3)}) ?
The derivative of 1/(2sqrt(x)+1/(3x^{2/3)}) is -1/(4x^{3/2)}-2/(9x^{5/3)}
What is the first derivative of 1/(2sqrt(x)+1/(3x^{2/3)}) ?
The first derivative of 1/(2sqrt(x)+1/(3x^{2/3)}) is -1/(4x^{3/2)}-2/(9x^{5/3)}