What is the derivative of 1/(2sqrt(r))+1/(6r^{5/6)} ?

The derivative of 1/(2sqrt(r))+1/(6r^{5/6)} is -1/(4r^{3/2)}-5/(36r^{11/6)}

What is the first derivative of 1/(2sqrt(r))+1/(6r^{5/6)} ?

The first derivative of 1/(2sqrt(r))+1/(6r^{5/6)} is -1/(4r^{3/2)}-5/(36r^{11/6)}

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derivative of

\frac{1}{2 r} + \frac{1}{6 r ^{\frac{5}{6}}}

- \frac{1}{4 r ^{\frac{3}{2}}} - \frac{5}{36 r ^{\frac{11}{6}}}

Solution steps

\frac{d}{d r} (\frac{1}{2 r} + \frac{1}{6 r ^{\frac{5}{6}}})

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}{6 r ^{\frac{5}{6}}})

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

\frac{d}{d r} (\frac{1}{6 r ^{\frac{5}{6}}}) = - \frac{5}{36 r ^{\frac{11}{6}}}

= - \frac{1}{4 r ^{\frac{3}{2}}} - \frac{5}{36 r ^{\frac{11}{6}}}

\frac{( x + 2 ) ( 2 x + 4 )}{- x ^{2} - x - 2}

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\frac{d}{d x} (ln (\frac{( 2 x + 9 ) ^{3}}{x ^{2}}))

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What is the derivative of 1/(2sqrt(r))+1/(6r^{5/6)} ?
The derivative of 1/(2sqrt(r))+1/(6r^{5/6)} is -1/(4r^{3/2)}-5/(36r^{11/6)}
What is the first derivative of 1/(2sqrt(r))+1/(6r^{5/6)} ?
The first derivative of 1/(2sqrt(r))+1/(6r^{5/6)} is -1/(4r^{3/2)}-5/(36r^{11/6)}