What is the d/(d{r)}(1/(2sqrt({r))}+1/(3{r)^{2/3}}) ?

The d/(d{r)}(1/(2sqrt({r))}+1/(3{r)^{2/3}}) is -1/(4{r)^{3/2}}-2/(9{r)^{5/3}}

What is the first d/(d{r)}(1/(2sqrt({r))}+1/(3{r)^{2/3}}) ?

The first d/(d{r)}(1/(2sqrt({r))}+1/(3{r)^{2/3}}) is -1/(4{r)^{3/2}}-2/(9{r)^{5/3}}

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

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

Solution steps

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

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}{3 r ^{\frac{2}{3}}})

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

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

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

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