What is the derivative of 1/(2sqrt(x)+1/(9x^{8/9)}) ?

The derivative of 1/(2sqrt(x)+1/(9x^{8/9)}) is -1/(4x^{3/2)}-8/(81x^{17/9)}

What is the first derivative of 1/(2sqrt(x)+1/(9x^{8/9)}) ?

The first derivative of 1/(2sqrt(x)+1/(9x^{8/9)}) is -1/(4x^{3/2)}-8/(81x^{17/9)}

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\frac{d}{d x} (\frac{1}{2 x} + \frac{1}{9 x ^{\frac{8}{9}}})

- \frac{1}{4 x ^{\frac{3}{2}}} - \frac{8}{81 x ^{\frac{17}{9}}}

Solution steps

\frac{d}{d x} (\frac{1}{2 x} + \frac{1}{9 x ^{\frac{8}{9}}})

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}{9 x ^{\frac{8}{9}}})

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

\frac{d}{d x} (\frac{1}{9 x ^{\frac{8}{9}}}) = - \frac{8}{81 x ^{\frac{17}{9}}}

= - \frac{1}{4 x ^{\frac{3}{2}}} - \frac{8}{81 x ^{\frac{17}{9}}}

What is the derivative of 1/(2sqrt(x)+1/(9x^{8/9)}) ?
The derivative of 1/(2sqrt(x)+1/(9x^{8/9)}) is -1/(4x^{3/2)}-8/(81x^{17/9)}
What is the first derivative of 1/(2sqrt(x)+1/(9x^{8/9)}) ?
The first derivative of 1/(2sqrt(x)+1/(9x^{8/9)}) is -1/(4x^{3/2)}-8/(81x^{17/9)}