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

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

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

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

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derivative of

\frac{1}{2 r} + \frac{1}{9 r ^{\frac{8}{9}}}

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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