What is the d/(dv)(sqrt(u/v)) ?

The d/(dv)(sqrt(u/v)) is -(sqrt(u))/(2v^{3/2)}

What is the first d/(dv)(sqrt(u/v)) ?

The first d/(dv)(sqrt(u/v)) is -(sqrt(u))/(2v^{3/2)}

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\frac{d}{d v} (\frac{u}{v})

- \frac{u}{2 v ^{\frac{3}{2}}}

Solution steps

\frac{d}{d v} (\frac{u}{v})

Treat

u

as a constant

Apply the chain rule:

\frac{1}{2 \frac{u}{v}} \frac{d}{d v} (\frac{u}{v})

= \frac{1}{2 \frac{u}{v}} \frac{d}{d v} (\frac{u}{v})

\frac{d}{d v} (\frac{u}{v}) = - \frac{u}{v ^{2}}

= \frac{1}{2 \frac{u}{v}} (- \frac{u}{v ^{2}})

Simplify

\frac{1}{2 \frac{u}{v}} (- \frac{u}{v ^{2}}) : - \frac{u}{2 v ^{\frac{3}{2}}}

= - \frac{u}{2 v ^{\frac{3}{2}}}

What is the d/(dv)(sqrt(u/v)) ?
The d/(dv)(sqrt(u/v)) is -(sqrt(u))/(2v^{3/2)}
What is the first d/(dv)(sqrt(u/v)) ?
The first d/(dv)(sqrt(u/v)) is -(sqrt(u))/(2v^{3/2)}